My husband may have the same thing you are referring to. He has had GERD symptoms for a couple of years now. Prilosec, Pepcid, etc. meds are not effective for him. His esophagus muscle does not work properly to move food and liquid down to his stomach, thus causing regurgitation. The acid backs up into his lungs. The irritation and immflamation from that causes him to cough up quite a bit of blood on a daily basis throughout the day. I should also mention he has bronchiectasis, which is a lung disease. We go back to the pulmonologist in a couple weeks for another ct scan, bronchcoscopy, and to meet with a surgeon to talk about his options. I hope some of this helps you on your quest to find answers for yourself. Good Luck!
Your doctors are probably right about the likelihood that the cause of your bleeding is nothing to worry about. However, if you haven't had a CT scan or MRI of your nose and sinuses, you should ask your doctor about it. You might also ask the ENT if you could switch to a different medicine to see if that would stop your chest discomfort. Finally, you and your doctors should not assume that the blood is coming from the upper airways. It could be coming from your lungs. After 6 months, this possibility should not be ignored.
I forgot to mention that before sending me to an ENT, my doctor had me get a chest x-ray when my problems first started occuring that came back normal.
I have also had on and off anxiety since my problems have become persistent. I can imagine axiety might make the discomfort in my chest worse, but I don't think anxiety would explain blood in the mucus.