While I haven't had a C-Section I've had a a few Operations, try gently rubbing the scar every day with your hands , and fingers or as often as you can remember. This will help the nerves heal, and stop going "pain ouch" (which the burning sensation is my surgeons explained) when there is nothing there, and form normal connections again in the skin to touch.

Does take awhile but can help alieviate that sensation ones the new nerves grow in. Months sometimes. If you dont touch the scar at all, the nerves will not learn and not form normal touch connections and it will continue to give of pain when touched or that burning sensation.

I've had to do this for my knee reconstruction and my gall bladder operation and the scars now dont have weird sensations and respond to touch like normal skin.

HTH