It looks like a typical ECM lesion. The Drs. already think it is infected, hence the doxycycline. Even if it was a cellulitis, doxycycline would cove the common pathogens.
Bob
I would go back and have them take another look
Please reconsult Infectious Disease for reassessment.
I'm not a Dr. so your milage may vary.
Ixodes rinicus, the wood tick or black-legged deer tick in know to be a primary carrier of Lyme's Disease. Doxycycline is a pretty broad spectrum antibiotic that should cover Borrelia infection. Other tick-borne infections may be transmitted simultaneously with Lyme, including Bartonella, Babesiosis, Ehrlichiosis, and Rickettsia.
Acute (early) symptoms: "bull's-eye" rash (erythema migrans) - a circle or ring of inflamed skin surrounding the initial tick bite) or papular (raised) rash, fever, malaise, fatigue, headache, muscle and joint aches in large joints, sore throat, sinus infection, paralysis - usually associated with Lyme meningitis or Rocky Mountain spotted fever.
Traditional treatment of acute Lyme disease usually consists of a minimum two-week to one-month course of antibiotics, preferably doxycycline.