I also don't think in this case it's a matter of "rights" on either side. I'm sure, had you known you would be sharing a car with someone who is allergic to perfume, you would not have worn it.
Given that you weren't aware of her allergy, I actually think it was rather rude of the woman to make such a song and dance about it. If it was such an issue for her, she should not have accepted a lift. I agree with petallus that her reaction sounds like attention-seeking.
I had a work colleague who found that she became very nauseous and got an awful headache if someone was wearing Opium. Once people knew, out of consideration, they stopped wearing it at work. I'm not sure what I would have done if a colleague had been allergic to other people's make up - I'd have probably got another job rather than have people tell me how ill/tired/awful I looked!