I have come close to fainting a lot of times during panic attacks and I have actually fainted occasionally as well. In my case I noticed that my breathing becomes shallow and quick in an anxiety inducing situation. Then I feel very warm and there is also some sort of pressure on my heart (like it's being squeezed). This sensation can also be accompanied by tingling in my hands, numbness, ringing in the years, tunnel view or blurry view, derealization etc. It depends on the situation. The one time I fainted it happened so quickly that I didn't have time to react. So although its rare, a person may faint from hyperventilating for too long. At least once you faint, your breathing resumes to the 'normal' pace.
The best thing I can do is to stay aware of the breathing, because once you learn to control the breathing you can eliminate a great deal of anxiety and also avoid getting alkalosis and feeling lightheaded. I also try to avoid too much caffeine or foods containing too much sugar. I'm sure you have been told this enough but drinking plenty of water is obviously very important.
When I started having anxiety problems I got tested for all sorts of things including MS, heart issues, diabetes, endocrinological issues etc. I would definitely recommend that you do the same just to rule out a possible medical issue.
Once you have done that you can focus on dealing with these problems. This is just my opinion based on my experience but some people tend to have an overly sensitive vagus nerve. The most common reason is because they are stressed out and out of balance. There are many exercises you can practice everyday in order to regain your balance, such as deep belly breathing, certain yoga exercises. I wish you good luck in managing your problems and hope things get better for you