Am I right for wanting to reject this job offer?

Two possibilities:
1. Call them, explain your situation, ask if it would be okay with them if you could start a couple of days later. As long as you explain your reason for the request - and it IS a very good reason - they can hopefully be okay with that, and you won't have to quit a job over this.
2. If I understand you correctly, I get the impression that the driving is the main dangerous issue here. Could that be solved somehow, either by using public transportation until your medication is in order or getting a friend or family member to drive you? Then, at work, again explain your situation, and do your work as best you can but TAKE BREAKS when you get dizzy and think it could go bad.
Whatever happens, good luck.
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