You could take a photo of it right after you finish your ride and take that with you to the dermatologist's office. That way, she could see what you're talking about. But first, I'd try the cortisone cream.

People do "grow into" (and "out of") allergies, btw. Just because you haven't had sensitive skin for most of your life doesn't mean you can't develop some sensitivities now. I went through some miserable skin problems during menopause, and cortisone--and waiting for my hormones to quiet down--were the only things that helped.