As I mentioned earlier, serology does NOT demonstrate active Lyme disease. It demonstrates exposure to it. Lyme serologies use an enzyme-linked immunosorbent assay to test for IgG antibodies to Lyme (a Lyme titre). If this is detected, then it is confirmed by a Western blot. Very few laboratories are able to test for IgM antibodies to Lyme (which would imply a more active or recent infection). Where I worked, we were able to do IgM antibodies. Where I work now we aren't able to do them. In cases of active disease, this titre is elevated in about 70% of individuals. The remainder have only a small baseline titre.
Yes, you are correct. Lyme disease is a clinical diagnosis. I frequently diagnosed it based on rash, Bell's palsy presentation, etc. However, neuroborreliosis is isolated to neural tissue, and it requires a lumbar puncture to demonstrate Lyme being present in the cerebrospinal fluid. One can suspect neuroborreliosis, but to definitively diagnose it, you require a lumbar puncture. It's like diagnosing someone with a MRSA abscess -- you can suspect it and treat it, but you can only definitively diagnose MRSA with a culture swab and antibiotic sensitivities. To diagnose you with neuroborreliosis without CSF B. borgdoferi antibody index is really doing yourself a disservice.
LLMD? That must be a Canadian term. There is no board-specialty certification process for Lyme-trained physicians in the US. However, the hospital I worked at was the US leader in Lyme research.
Remember, antibiotics are not without side effects. You will likely think much differently about the benign nature of antibiotics if you develop C. difficile colitis from them.
You really should do more research prior to your antibiotics. Steroids have shown benefit in people with post-Lyme disorder. Antibiotics are pointless for post-Lyme, and a PICC line is not a benign thing. I've seen my fair share of people with clots, infections, etc. (I'm not talking about line clots; I'm talking about DVT's.)