BS”D
I would hope you were tested for Lyme Disease but after my year of collecting useless creams due to a subjective medical error, I would always triple check. Sometimes even the most thorough doctor can miss something or use incorrect judgment when diagnosing an illness.
Off the top of my head, yes, the organism that causes Lyme does cause skin problems as part of the disease process.
Swimming is probably the best exercise for you because it has the lowest impact on your already compromised joints.