My ENT has missed several sinus infections when I knew that's what was going on. The neurologist he sent me to sent me for a head scan which showed blocked, full sinus. I finally was put on antibiotics, but they never cure everything completely. Yeah, the dizziness can be a symptom also.
I use sinus wash every day in winter just to clean sinuses out and stop infections from starting or lessen the effects. I get weekly allergy shots, which are lots better than allergy misery.
Go see the neurologist. At least he can rule out migraine. Your symptoms COULD also be migraine. Or, you could have both.
Go to a GOOD allergist and get some new testing. New rules say re-test every 3 years