S.W.
I've never done biofeedback for my migraines, but what worked great for me is a chiropractor. Many doctors don't recommend chiropractors because they don't understand the methods used or were taught in antiquated med school that chiropractors = hokey medicine. My doctor said that if it gave me relief from my headaches, she saw no problem with it. And, it worked great for me! My chiropractor even gave me her cell phone so that she could squeeze me in for an adjustment any time I felt a headache coming on. It almost always worked for me. I'm with you... the medicines they have for migraines are very powerful even for adults, much less kids. I take imitrex nasal spray only if I'm at the point of vomiting and can't keep traditional pain killers down.
I'm a bit surprised that your doctor suggested biofeedback. It's considered alternative medicine and I personally know someone (a relative of a friend) who has NO medical training, but invested in a biofeedback machine and "uses" it to help "diagnose" people. If I were to try alternative medicine, biofeedback would not be my first choice.