Ring worm is very different from the Lyme bull's eye rash, and it doesn't leave a black mark in the center.
There is a type of bulls eye that leaves a black mark like what you have described, Gorby, although I can't remember the details right now. Are you sure that the tick's mouth parts were cleanly removed? If not that would explain the puss as well.
Treating with Acupuncture, Traditional & Modern Chinese Medicine & Western Herbs. Before tx, I had all but 20 of the symptoms on the "Master Symptom List" for Lyme disease.
"Absence of proof is not proof of absence" - Dr. Edwin Masters, great LLMD & researcher -RIP
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