I have experienced dizziness and balance issues a few times (!), but true vertigo, only once. It came on very suddenly at work one afternoon - I didn't actually associate it with ms immediately, as ms hadn't been a big issue for me prior to that. I was really scared as the world was literally spinning, accompanied by bad nausea - very, very frightening.
My colleagues carted me off to the emergency room at a hospital near where I worked, and it was only after going through a work-up and almost being given a diagnosis of 'panic attack' (my BP was very high and I normally have low BP, it was natural for it to be high because of my fear though, but paradoxically, the medical staff thought that anxiety was the issue, instead of it being caused by the world literally spinning) - when it eventually came out that I had MS (this was when it was still quite mild, before I started Avonex, and they never asked and I never thought to mention it during my exam), I was referred to my neuro, who diagnosed the vertigo.
He admitted me and gave me some drug IV (can't remember what it was) and it improved rapidly in about 36 hours and I went home.
Thank God I have never had it since (this was about 3 years ago, and I can still remember it very clearly) - it is a truly awful thing that totally prostrates you, you cannot even get to the toilet.
I really feel for you - I still have balance issues and occasional dizziness, but vertigo is a completely different animal.
I believe that the folks who suffer from Menieres disease (spelling - an affliction of the middle or inner ear) can suffer from vertigo too - maybe the drugs used for this would help you? I remember they use anti-emetics like Stemetil, and motion sickness drugs too...? But these also have side effects...
I can understand your concern regarding safety - maybe you should drive with someone in the car with you (just in case) for a few months until you have tracked the occurrance of the vertigo and can judge its' impact on your driving capabilities?
The distinction between dizziness and vertigo was made clear to me after I researched it - which I did after experiencing it.
I wish you all the best.