sounds just like around here (regarding new patient appointments) and you just have no choice but to wait it out if it ain't life threatening, but once you're in, you're in.
one thing i did one time was take a photo of my rash which has been somewhat helpful with doctors as time goes on (a picture's worth a thousand words), so maybe you could take some good photos, take them with you to the appointment. just an idea, but if i ever have another rash, that's what i will do again, even if i can get right in to see the dermatologist, then i can show them to any doctor in the future. too bad we can't take similar photos of our insides with our own cameras

good luck with the appointment!