You are already far beyond the need for using an entrainment product as a meditation aid. Those who sincerely believe this to be the case would not have come searching for a meditation site such as Project Meditation to help them learn and practice meditation and brainwave entrainment. They would probably not even bother with using an entrainment aid; hence this entire discussion would be irrelevant to them. The fact that you are here, reading this, seeking to benefit from incorporating meditation and brainwave entrainment to aid in your existing meditation practice suggests you are not one of these folks whose development is so advanced that entrainment is of no use to you.
The reason this rule of thumb is so useful is because there is a huge market for simple answers. A genuine elegant solution (one that accomplishes more with less) is highly valuable in the marketplace. We are used to technology delivering new easy solutions to previously difficult tasks. While most improvements are incremental, there are occasional breakthroughs that transform our lives.
This is not to say that entrainment cannot produce some physical effects, particularly negative ones. It is possible to induce epileptic seizures using entrainment, especially visual entrainment that employs flashing lights. That’s why people with seizure disorders are uniformly told to consult with their health care provider before using entrainment if they have a seizure disorder or some other serious medical condition.
Binaural beats, or binaural tones, are auditory processing artifacts (apparent sounds) resulting from the stimulation of the ears with two different sound frequencies. In fact, when two different vibrations are delivered to the brain separately through each ear, using stereo headphones, the two hemispheres of the brain function together to “hear” and perceive not the external sound signals, but a third phantom signal. This resulting signal, discovered in 1839 by Heinrich Wilhelm Dove, is called “binaural beat”. The effect on the brain waves depends on the difference of each tone. For example, if a sound frequency of 300 Hz is played in the left ear and 307 Hz in the right one, then the binaural beat would have a frequency of 7 Hz (“frequency following response”) which corresponds to the Alpha brain state, generally associated with relaxation, visualization and creativity. The beating tone is perceived as if the two tones mixed naturally, out of the brain. For the binaural beat effect to occur, the difference between the two frequencies must be small (less than or equal to 30 Hz), otherwise, the two tones will be heard separately, and no beat will be perceived.
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. :)

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.
Binaural beats are acoustically generated frequencies that match the frequency bands of brain waves and are therefore considered a means to inducing neurophysiological relaxation. There is, however, large dispute on the scientific quality and validity of extant research on binaural beats. Thus, the effect of a binaural 10Hz (Alpha) stimulation on subjective and physiological parameters... [Show full abstract]
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.