Are you in the US now, or somewhere else? There are different strains of Lyme and similar diseases in different parts of the world.
Your rash could be a new infection, and it could be a new infection with Lyme, or your old infection becoming active again after your more recent bite.
Different co-infections (meaning infections that come from the same ticks that carry Lyme) sometimes need drugs different from the drugs that treat Lyme. That could be a reason you don't feel you are reacting to the meds you are on now.
Also, co-infections require different blood tests from Lyme.
I would suggest you look around on line for photos that look like your rash, so that you can talk to your MD about further testing. The common co-infections are Rickettsia (also called ehrlichiosis), Babesiosis, bartonella, mycoplasma, and a few others.
If you google (or otherwise search online) for images of 'flat red rash' or each name of the co-infections above, it might give you some ideas to present to your doctor.
I hope you are feeling better soon ... and by the way, your English is excellent, and needless to say, much better than my Romanian. :) Let us know how you do, okay?
And I forgot to say the most important thing:
Call your doctor's office and tell them about the rash. It might be a reaction to the medication you are on.