I'm not sure how much of a drive any of these will be for you, but for what it's worth...a lady who runs a local Lyme disease support group gave me this list of doctors when our daughter was bitten by a deer tick a month or so ago. I'm not sure which ones of these will treat children...one is listed as a pediatrician though. We ended up taking our daughter to our family doctor because no one on this list could see her soon enough. Our Dr. prescribed 4 weeks of antibiotics without a positive test. But she was on antibiotics the day after the tick bite so I think we caught it early enough. I know I've seen a website that listed Lyme-friendly doctors in the U.S. Maybe if you do a search you could find it?
Dr. Mark Sivieri, Laurel, MD 301-490-9911
Dr. James Matthews, Gaithersburg, MD 301-216-2065
Pediatrician Dr. Alan Vinitsky, Gaithersburg, MD 301-840-0002
Dr. Norton Fishman, Rockville, MD 301-330-9430
Dr. Letitia Short, Towson, MD 410-337-2707
Dr. Kenneth Singleton, Lutherville, MD 410-296-3737
Dr. Elisabeth Lucas, Lutherville, MD 410-823-3101
Dr. Richard Berg, Lutherville, MD 410-583-2711
Dr. Julia Wen, Lutherville, MD 410-583-2711
Dr. Sarah Fletcher, Sterling, VA 703-421-7000
Dr. Leila Zackrison, Fairfax, VA 703-359-9300
Dr. Trent Nichols, Hanover, PA 717-632-0300