Perscribed 10 days docycyline

I'm really confused. I have been sick for 2 years and have an undiagnosed movement disorder. I just received a positive tier 1 test for IgM/IgG. The tier 2 indicated negative. My doctor prescribed 10 days of doxy. for context I had a rash from a bite on my back around the onset of my symptoms and recently had a tick bite on my stomach in the last 2 weeks.

whether it is an old infection or a new injection, would 10 days of antibiotics work?

what is up with the tier 2 tests saying negative?