No, Lyme and mold do not go hand in hand. I have had Lyme for over 45 years, and live in northern Arkansas (where even the cars will grow mold on them!) and have never had any mold issues. It's more up to how the body handles mold, not just if you have been exposed to it when you have these infections.
I would encourage you to NOT have a blood test done for Fibro - as it will NOT rule out Lyme, but will likely convince any doctor that's what you have. They didn't have a blood test when I was diagnosed with Fibro, and it's still a hard diagnosis to shake.
The new test for Fibro:
"Recent data highlight the role of the immune system in FM. Aberrant expressions of immune mediators, such as cytokines, have been linked to the pathogenesis and traits of FM. We therefore determined whether cytokine production by immune cells is altered in FM patients by comparing the cellular responses to mitogenic activators of stimulated blood mononuclear cells of a large number of patients with FM to those of healthy matched individuals."
bmcclinpathol.biomedcentral.com/articles/10.1186/1472-6890-12-25 As if Fibro patients just randomly have high cytokines.....
I would agree with the other members saying to just find your other options - don't rely on these docs that you are seeing to get you into a good treatment for Lyme, much less be able to diagnose you properly.