Does the skin actually blister or even show any signs of distress and friction?
- If yes, then I would use petroleum jelly between the toes before running.
- If no, then it sounds like a nerve issue that makes it feel like the toes are burning up.
I've had both conditions, and needless to say, the nerve issue is harder to diagnose and solve (chiropractor and/or orthopedic surgeon).
Keep us posted.
Best regards,
Dale