First of all, keep in mind that I am unable to diagnose you because I am unable to examine you, this forum is for educational purposes. From the symptoms you provided it is likely that you have migraine headaches (or migraine equivalents). Migraine headaches can occur with symptoms without actual head pain (migraine equivalents) Most headache experts no longer believe that "sinus headaches" exist. Of course a headache can be a symptom of acute sinusitis (fever, purulent nasal discharge, facial pain), but is unlikely that sinus problems cause chronic headaches. These headaches often turn out to be migraines. One of the frequent symptoms of migraines is Dizziness.
That being said, you should have an MRI brain with contrast to rule out other pathology (CT is not adequate).
In addition it sounds like you have serious problems with your sinuses that I would leave to the discression to your ENT for management. I would not expect your symptoms to go away after the surgery, but they may if it is your sinuses that are triggering migraine headaches.
I would recommend that you see a Neurologist that specializes in headaches to further evaluate your head sensations and dizziness.