Can headaches and skin burning sensation have any relation to each other?

It depends on cause: It depends on the cause of your headache.There are many neurological conditions where you may have both these.But if it is simple occasional headache then the answer is no

Burn Baby, Burn...: An interesting topic & the answer is"yes."Usually this sensation, along with a laundry list of other sensations, is associated with so-called"migraine"headaches( a broad spectrum of symptoms). The skin "burning"(or other weird feelings, called "dysesthesias") is thought to be due to nerve signals from areas other than those that cause the "classic" symptoms of migraine (throbbing pain, auras, etc)