It sounds like your brain might have initial trouble adapting to the binaural beats. The same thing happened to me when I listen to the Beta frequency (I got a headache), but then I discovered that I had the volume turned up too loud. I would say experiment with these frequencies, but at a low volume. See how you go. And if you continue to have anxiety, by all means, stop listening. Also, not all binaural beats are created equally. Some are amateurish, but the ones from Binaural Beats Meditation (mentioned and linked to in this article), are professionally created and the ones that I personally listen to. I love them (especially the Theta/Delta ones)! I hope this helps. :)
For our ancestors, stress was a survival skill during brief, life threatening situations. Once the danger passed, their stress levels lowered. However, in today’s world, we are constantly bombarded by stressors, such as work deadlines, traffic, and family obligations. We rarely get a break long enough to relax and relieve the stress. The over-activation of our stress hormones have been linked to high blood pressure, heart attacks, lower immunity, depression, anxiety, and more.

A common element in recordings incorporating alpha and theta frequencies is a steady but barely perceptible rhythm of the frequencies themselves. This subtle and calming pulse mixes with sounds of gentle breezes, distant bird songs, and the slow progression of deep synth notes. Underneath this, below the audible sounds at sub 16 hertz levels, other frequencies intermingle, deepening the merging of conscious and unconscious mind.
Today, EEG machines are used for diagnosing epilepsy and sleep disorders, for determining dosages for anesthesia, and measuring the brain activity of people in comas or suffering from brain trauma. EEG machines also continue to play a role in researching and understanding brainwave entrainment and developing new and better methods for delivering the benefits of this form of brainwave modification. 

Words could be great stress relievers. One technique to quell sudden stress is to repeat a phrase from which you draw power and strength. “Think positively about releasing what is bothering you by repeating a positive mantra that uplifts you such as, ‘I am at peace,’ ‘All is well,’ ‘I choose to think thoughts that serve me,’ or ‘I love and believe in myself fully,’” says Carol Whitaker, life transformation expert and the author of Ridiculously Happy! The Secret to Manifesting the Life and Body of Your Dreams. “This too shall pass” is another good one. Repeating a mantra is actually a type of meditation that can make you more resilient to stress—some studies show it can actually alter your brain’s neural pathways. You can place reminders of your mantras near the places you tend to get stressed, like your work space. “I actually keep a file on my computer of great quotes and inspiring sayings. So when I’m feeling overwhelmed by life’s struggles, I clip them to my screensaver, post them on my social media, and even print them out to put on my refrigerator or desk,” Dr. Serani says.
Fortunately, the recommendations for exercise in the role of stress management fit with the current health recommendations (12). The proposed physiological adaptations thought to improve the way the body handles stress and recovers from stress can occur with a regular moderate to vigorous aerobic exercise program (12,13,16), such as the recommendations of 150 minutes of moderate-intensity aerobic exercise per week or 75 minutes of vigorous-intensity aerobic exercise per week. If an individual is using exercise as a time-out from stressors, shorter duration activity can serve the purpose, especially when lack of time or fatigue is a concern. Consider an individual who reports significant work-related stress. Breaking the exercise into two 10- to 15-minute sessions, one before work and one at lunch time when possible, can help combat stress throughout the day. Although there is not a lot of research with resistance exercise and stress management, resistance exercise can be used to provide a time-out from one’s stressors. Because resistance training produces different exercise adaptations compared with aerobic exercise, it might not affect the way the body physiologically reacts to stress as aerobic exercise does. However, the acute effect of a time-out to reduce stress can be beneficial. In addition, clients can receive the numerous health benefits associated with resistance training. The resistance exercise prescription for general health benefits of 2 to 3 days of exercise to target all of the major muscle groups performed at a moderate intensity of 8 to 12 repetitions can be recommended.
They came to the table with the idea that the entrainment track would “cause” them to be in meditation, which it doesn’t. Or they thought that having the specific brainwaves the entrainment program promotes would “cause” them to be in meditation. It doesn’t. If you really understand the principles above, you’ll understand why. If you don’t grasp why yet, read these principles again and consider what they really mean. The answer is there.

Brain wave entrainment is a real phenomenon and is useful as one method of investigating how the brain works. But there is no evidence, nor any theoretical basis, for any long lasting effect on brain function or that there is any benefit of any kind. Despite this, there is a huge industry of devices that claim to train your brain waves and have a beneficial effect. I wouldn’t waste a dime on any such device.
Everyone experiences stress, and not all stress is bad. Individuals who experience acute episodic or chronic stress are at increased risk for developing stress-related health problems. Research supports the idea that exercise can improve the way the body handles stress, and it can provide a time-out from stressors. Exercise programs meeting the current recommendations for health included within a stress management program can be effective in stress reduction. However, it is important to consider the client’s stressors and physical activity barriers, activities the client will enjoy, and the exercise setting. Prescribing exercise for clients seeking stress management is recommended, but fitness professionals should recognize that some clients will need additional assistance for managing stress and major life stressors.

A crossover RCT of a single session of theta stimulation in four healthy adults reported no significant improvement in verbal fluency or attention associated with the intervention and a reduction in immediate recall. Controlled comparisons reported significant benefit from the intervention in all three outcomes measured. Six pre/post studies reported significant benefit from the intervention for 19 of 28 cognitive outcomes.
Binaural Beats or “binaural tones” are created by playing slightly different frequencies separately into each ear. The difference between the two frequencies stimulates a response in the brain which correlates with this frequency difference. For example, if we present a 100 Hz tone to the left ear and a 105 Hz tone to the right ear, a frequency of 5 Hz is stimulated. This is what is known as the “frequency following response”.

♥ ← This set of tones with the bird calls from Aotearoa is keeping me awake while I finish an essay I've been working on for the past four days. Focus beats + sounds I associate with morning = wakefulness. Still craving the bed, but at least I'm not falling asleep at my desk. Thanks myNoise, without you I'd probably be listening to music and distracted.

In 1956, the famous neuroscientist W. Gray Walter published the results of studying thousands of test subjects using photic stimulation, showing their change in mental and emotional states. He also learned that photic stimulation not only altered brainwaves, but that these changes were occurring in areas of the brain outside of vision. In Walter’s words:

If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.