I had burning for months too. It was all over my body and even on my scalp.
I had persistent burning in my forearms for months, not unlike a fresh sunburn feeling. I also get more fleeting burning sensations in my face and legs. In addition, I also get burning feelings deep in my joints, esp. when I am getting up in the morning.
I was on neurontin for awhile, and it helped cover up the symptom, but the cure is to treat the Lyme directly as you are doing. It can take time.