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. The symptoms you describe are very atypical, but it sounds that you are in a lot of pain. Some headaches such as migraines can become so severe that they occur all of the time (so called "Status Migrainosis"). These type of headaches generally require IV medications including DHE (Dihydroergotamine), Depakote, Magnesium, Benadryl and Kytril to stop these headaches. It is hard to explain your pain by a headache syndrome alone (for example the only way to have 24/7 pain for 5 years is not to sleep for 5 years). This type of history is often obtained when someone has severe pain that is then amplified by depression. Depression makes pain much worse and the headaches WILL NOT get better until the depression is treated (even if you dont "feel depressed").
Your nasal inflammation may be triggering headaches, but also may be unrelated.
I would recommend that you see a neurologist that specializes in headache and has an IV infusion suite available. You will likely need 3-5 days of intensive IV medications (DHE protocol) to break the cycle of your headaches. I would also start anti-depression medication to help with any possible amplification of your pain (Effexor or Lexapro would be a good choice). I hope this has been helpful.
please try alternative therapies like acupuncture, reiki and YOGA