Burning sensations on face that sometimes occur with a read rash and sometimes does not. What is this?

Your experience is unusual and difficult.   Your symptoms of a burning sensation and an intermittent rash are weird. Weird, because it is difficult to know what is causing it.  Physicians would first try and see if any medications you are taking may be contributing to the problem.  This is NOT related to the nasal surgery.  I advise contacting your internist to evaluate or at least start checking for different causes.  The best way to figure this out would be to develop a relationship with a physician who is interested in helping you figure this out.