Thanks for posting your query at DoctorSpring.com
I can understand your concern. I reviewed the picture.
At present , the rash is not characteristic for Lyme's disease. However it could be the initial stage and may slowly progress and form the characteristic rash of Lyme's disease.
It would be the best to treat it with antibiotics that would treat Lyme's disease as well as a bacterial infection which it currently looks like.
I would recommend getting a prescription from your doctor for an oral antibiotic like cefuroxime or amoxicillin- clavulanate. Regular follw ups with your dermatologist to see the improvement of the lesion would be important.
Please let me know if you have any queries.