Hi there, Thanks for writing in. I read your question with diligence. Throbbing burning pain suggests involvement of blood vessels and sensory nerves to feet. Feet are hot to touch, there is swelling and swollen veins suggest some kind of possible infection or vasculitis
process. Please do not distress yourself but be active. No matter what time of day or night it is child will find relief when a doctor does a complete physical examination if need be certain tests. Only appropriate medicines can bring relief. My suggestion will be taking the child to emergency room at the soonest. If you are writing from US please call 911. If from Australia call 000. Good Luck.
With Best Wishes
Dr Anil Grover,
Medical Specialist & Cardiologist
M.B.;B.S, M.D. (Internal Medicine) D.M.(Cardiology)