I experienced a bad bout with cellulitus last year. Mine came from cleaning out a hot tub while I had a bad case of psoriasis on both ankles. (Lesson - don't ever do this.) You're right - the burning is horrendous! Since it started on a weekend, I tried the 'doc in the box' first. They gave me the standard antibiotics. That didn't do much good. I was given a different prescription for antibiotics. Again, not much success, but the cellulitus was climbing up my legs. And the burning! I ended up going to the emergency room at 3 in the morning (great time to go as no one else was there) and was put in the hospital with intravenous antibiotics and oral steroids. At least that stopped the growth of the cellulitus. It actually took quite a while (couple of weeks) for the cellulitus to disappear. At one point, my doctor wanted to take a 'punch biopsy' (sounds horrible, doesn't it?) because it wasn't clearing up as fast as he thought it should. Thank goodness it started to show improvement before he made up his mind.
One of the things that helped me with the awful burning was wrapping my lower legs in kitchen towels that were soaked with cold water. The shock of the cold water at least took my mind off the burning for a short time.
Make sure you are under your doctor's care until this clears up. It can turn dangerous. I'm sending prayers your way.