One should have some idea of what levers one expects a doctor to pull. If a doctor isn't really engaging with your problem, then push towards those. Obviously you can't directly ask for them but rather focus on the right symptoms to nudge them there. You have to tiptoe around their ego.
And if you're wondering why you've got to learn to be your own doctor instead of relying on specialization of labor, well, welcome to our post-capitalist overfinancialized hellhole.
Also for this particular topic, you can send a tick in to UMass for testing and they'll tell you if it has Lyme and many other diseases. There's a bit of a turnaround time so it doesn't work for primary triage, but it's sure nice to find out that you're definitely in the clear.