this topic goes pretty deep
serology was pretty much all we had until recently and is still a mainstay of infectious disease testing.
but our immune systems have memory which means they typically hold some antibodies to just about
every pathogen we have ever encountered.
so then it becomes down to degrees of antibody response, and types of antibody as a means of trying to interpret the results. there are various issues with doing this.
bart is hard to test for full stop - even the best test on the market - Galaxy's latest method - multiple blood draws, culture in special medium, then parallel droplet PCR - only claims to be 50% sensitive according to their published work - and most other test houses use older technology which is lagging well behind.
clinical diagnosis is still probably the most reliable - but not easy
the best place to start i think is Burrascano's 2008 guidelines
https://lymediseaseassociation.org/wp-content/uploads/2009/08/burrguide200810.pdfif after reviewing that you are still unsure - i would do wither a therapeutic trial of a bart abx combo - or shell out for the galaxy test.