My mom was bitten by a tick in Colorado and given a 2 week course of antibiotics when she started to feel ill. She got better then promptly got worse as soon as they ran out. Over the next six months she progressively worsened until she could only get out of bed for a couple hours a day. Finally she found out about Lyme disease - many doctors do not believe that it even occurs in Colorado so she didn't know what was wrong for the longest time. She found a doctor out of state that insurance would cover who would treat her. She was on heavy doses of oral antibiotics for four years and has never had a relapse, some 20 years later.
Yes, and no, at least not initially. I believe they repeated the test and it came back positive at a later date. So it seems likely that she got something from the tick, probably in part Lyme. The Lyme test is reputed to have a high false negative rate, not sure to what extent this is true.
Good luck on your treatment.