This is not medical advice, it is what works fairly well for ME. But, it's pretty benign stuff that is considered conventional. Consider my suggestions, and then run them by your Drs. to see if you should try them.
Dizziness is mitigated by vestibular suppressants. Anti-vert is a Rx for dizziness that works well. It takes a couple of hours to start working. It is available over the counter (I believe) as "Dramamine Less Drowsy". It will likely make you a bit drowsy, so don't take it if you are planning on operating a band saw. Anti-vert is an antihistamine. First generation antihistamnines, the ones that DO make you drowsy, are vestibular suppressants. Benedryl is another one that works well, though it doesn't occur to most people that it can be used for that. Most days I have no dizziness issues. Some days, I feel just a tiny bit of it and I take one 25mg of Benedryl. This is half the dose used for allergies, so it's not like this is some kind of radical drug binge. Anyway, one 25mg OTC Benedry works for most of the mild symptoms.
On a rare bad day, I need the anti-vert. Since it takes a while to work, I need to take Zophran to keep from vomiting. The Zophran is a friggin miracle. It's like an instant "off" switch for vomiting.
Diazepam and Lorazepam also work, but no better than anti-vert for me and are a "heavier" drug in my opinion. I doubt you would develop a dependency of either if you take one here and there, and they are great at relieving the anxiety that goes with all of this, but I just feel better about taking an antihistamine than a "drug" like valium.
The anxiety that goes along with all of this WILL get better in time. An occasional valium isn't the worst thing a person could do to ease the road we are on and I'm not judging anyone who takes them here and there. Heck, I take one every now and then when I'm dizzy and my neck is like a vice from dealing with all of this, it's just that benzodiazepiens are not a long term solution, so watch out for Drs that might over-prescribe them.