Absolutely. Binaural beats were first discovered over 150 years ago, and their use in brainwave entrainment audio has been the subject of a great deal of scientific exploration over the last 35 years in particular. Millions of people use brainwave entrainment music to enhance their quality of life and to experience deep relaxation. In fact, brainwave entrainment technology is now used for more than just meditation. It is also used by a variety of practitioners and private users for improving self-confidence, stress relief, pain management, relaxation, improving and concentration and improving the quality of one's sleep. If you would like to read an objective third party report on binaural beats, please refer to this Wikipedia article.
Entrainment is a physics principle in which one rhythmic system falls in synchrony with another rhythmic system. If you’ve ever found yourself moving your body to the beat of your favorite song, then you’ve experienced entrainment in its most basic form. Besides music, this principle can be found all around you, probably more than you realize. Here are a few examples:
Theta brainwaves in the frequency range of 6 to 9 hertz are known as thalpha waves because of their proximity to alpha waves. They are seen during states of high suggestibility, during hypnosis, and during paranormal experience and are also connected to an increase in human growth hormone (HGH) levels and higher blood flow to the brain. Theta brainwaves sit between the realms of the subconscious and conscious mind, making them an especially useful brainwave state for developing creative thinking, working through emotional problems, and integrating subconscious and conscious experience. 
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From a brainwave entrainment effectiveness perspective, it’s my understanding that the response from isochronic tones stimulation starts to diminish over 30Hz and that 40Hz is about the limit for using them. So from what I’ve read on the topic a 100Hz beat wouldn’t work, probably because it’s too fast for the brain to process and synchronise with it.
Recently developed entrainment software has been designed to correct specific imbalances in hemispheric activity associated with undesirable mind-states. For example, people suffering with depression often have more activity in the right hemisphere, and specially designed brainwave music decreases this activity while increasing activity in the left hemisphere, reducing depression.

Gaia Meditation Delta programs are specifically designed to: improve sleep and healing process. Effects happen at a very deep subconscious level, ideal for powerful reprogramming. If you’re in lack of sleep because you’re a busy business man or because you have insomnia etc., a few hours of our Delta waves programs will trick your brain into thinking it had all the restorative sleep it needs.

♥ I'm a tired law student always looking for a study boost. I like to put on the Alpha waves and mix this with classical music for research and writing. The "beats" help to drive the music and add a feeling of focus and energy even during slower/softer passages. If you get the levels matched properly, you never even hear them. Throw in a cup of coffee and you'll be ready to save the world. Cheers!

As to the second question raised in the above paragraph, audio with embedded binaural beats alters the electrochemical environment of the brain. This allows mind-consciousness to have different experiences. When the brain is entrained to lower frequencies and awareness is maintained, a unique state of consciousness emerges. This state is often referred to as hypnogogia "mind awake/body asleep."  
Gamma waves are the fastest of the brainwave frequencies (high frequency band of brainwave activity) which signifies the highest state of focus possible. They are associated with peak concentration and the brain’s optimal frequency for cognitive functioning – the 40 Hz frequency corresponds to a Schumann resonance band and many scientists, including Nobel Laureate Sir Francis Crick believe that it may be the key to the act of cognition. The Gamma state relates to simultaneous processing of information from different brain areas; information passes very rapidly.

Isochronic tones have only been proven to have an effect while you are listening to them, that’s why you won’t find me claiming anywhere that there are potentially positive long-term effects. Once the tones stop, your brainwaves are no longer being stimulated by the sound and so they stop being in sync with the tone frequency. For you to think you are still feeling the effects after all this time and from such a short time listening to them, I think it may be linked to anxiety. I know that some people who are new to this type of thing can build up a strong feeling of anxiety, after worrying about the potential effects brought on by fear of the unknown. I suspect the problem may be psychological with you worrying about the potential effects and keep repeating the experience from memory in your head. When you keep going over the same thing in your head like that and worrying about it, it’s easy to then spot other potential side-effects like how your nostrils and body temp is feeling, then making links back to that experience and labelling that as the reason. I think the best way to overcome this is to realise that the side-effects you are mentioning are completely unrelated, so there is nothing to worry about. These tracks are literally listened to for millions of hours a month on YouTube across loads of channels. If the effects lasted for a long time people would just listen for 5 minutes and come back in a couple of weeks. But people keep coming back to listen because that’s the only way to feel the benefit and effects…while you are listening to them. If you are unable to stop thinking and worrying about this on our own, I recommend that you speak to your doctor about it or a specialist in dealing with anxiety issues. I hope that helps.

Entrainment is like priming the pump of meditation. It doesn’t “cause” meditation any more than pouring that little bit of water into the pump initially “causes” water to appear in the well. The water was already there. The conditions for the pump to do its job just needed to be set up. What entrainment does is to create the conditions and the internal environment typically associated with meditation. You could get to that point without entrainment, certainly, but the entrainment allows you to get there quicker, more consistently, and to remain there for longer periods of time than you would ordinarily be capable of doing on your own.
You won’t recall ever being in this state, but it’s an incredibly important brainwave for your health. In this state, you will be deeply asleep, but not actively dreaming. Your body needs this state to heal and regenerate. On a daily basis, you’ll need to achieve this state when you sleep at night to make sure your body can heal itself. When you’re feeling really sick or your body and mind are working hard, you’ll want to stay in this state a little longer.
How does brainwave entrainment work? Consistent, precisely engineered audio frequencies in the form of binaural beats cause the brain’s frequencies to match the stimulus. Your brain perceives two beats with slightly different frequencies (which are inaudible to the ear) through your headphones. It takes the difference between the two, and matches its own frequency to it. This is called the “frequency following” response.

Delta (3hz – 0.2hz) – Deep, dreamless sleep. Intuition. Empathy. Brainwave expert Judith Pennington calls it the doorway to Universal Consciousness and “A radar that scans the environment and psychically picks up information and energy.” According to British physicist C. Maxwell Cade “There have been reports that delta waves appear at the onset of paranormal phenomena.” (More information can be found in Cade’s book The Awakened Mind)

The activity of neurons generate electric currents; and the synchronous action of neural ensembles in the cerebral cortex, comprising large numbers of neurons, produce macroscopic oscillations. These phenomena can be monitored and graphically documented by an electroencephalogram (EEG). The electroencephalographic representations of those oscillations are typically denoted by the term 'brainwaves' in common parlance.[4][5]