Antivert (meclazine) is sold over the counter as "Dramamine Reduced Drowsiness". It is an antihistamine so it is not "controlled" like narcotics. Since it is not an abused drug, your Dr should have no problem renewing your script with a phone call. Often, it doesn't take much to help. Even a half of a pill might do the trick. But, you need to take it as soon as you feel symptoms as it takes time, maybe even a couple of hours, to work.
Also, it may reduce your brain's ability to compensate, so I don't know that it is a permanent solution. I manage to get through the day with as little benedryl as possible and only take the antivert when I have an acute episode. A normal dose of benadryl is 50mg every four hours. I usually take 25mg of benadryl once in the morning and once at beadtime. I need this for my allergies anyway and it is no where near the max dosage so I don't worry about being loaded up on meds all the time. Also, I got used to the drowsinessand it doesn't really make me feel "stoned" like it did. A slight bit of drowsiness is much better than a dizzy attack IMO.
Anyway, it's something you can play around with and discuss with your Dr. It's "safe" in that it's not a benzo like valium or a narcotic. I only need a valium maybe a few times a year, one dose.
I realize my balance issues might be much less severe than yours, so I'm not trying to say "it works for me, so it will work for you", I'm just saying that it gives me relief and it is worth exploring since it may help you.
By knowing I have rescue meds on my keychain, I don't have to worry about leaving the house and having a dizzy, vommit fueled emergency somewhere. It's terrible when you feel a little "off" as you are about to walk out the door. Do you go? If you stay home, and you don't get sick and the feeling passes, you wasted the whole day. When you stay home, you have nothing to do but focus on your symptoms and can even make yourself sick by thinking about it so much.