I do not think this rash sounds like lyme. It does not normally last that long. Mine lasted about 4-6 weeks. I would see a specialist to check for allergies and autoimmune disorders. I would also get a lyme test in case these are secondary rashes related to lyme. I had the bullseye initially then I had and still have strange rashes but they are nothing like the initial bullseye. Did you have tick bites?
Sorry to hear about your ailment -- I'm not a medical professional, and Lyme has lots of different manifestations, but your symptoms I've not heard of before related to Lyme.
Have you asked your doctor if it's a systemic fungal infection you have that should perhaps be treated with oral medications instead of topical (on your skin)? In your situation, I'd make an appointment and go back to see him/her esp if you haven't been back for three months.
Good luck! Let us know what happens.