I'm a little confused about what you are getting "desperate for an answer," for. Is it the pain in your head/neck/eye and ear or is it the anxiety that has come from this illness or both?
If you have been seeing an EENT for a year and they have not been able to give you a diagnosis and treatment, I'd say it's time to find a different doctor. Your anxiety, in this instance, is totally understandable and not unrealistic. I'd be anxious, too.
You said that you've just noticed that the anxiety seems to follow the use of your NETI pot in the morning. If you are using the NETI pot correctly, you should not be getting any of the solution in your stomach. Or at the very least, just a drop or two which I can't think would make you "hot and anxious." I would suggest not using the NETI for a few days and see if that stops the problem. If it does, you need to discuss a possible adverse reaction with your doctor. If it doesn't, you need to discuss your anxiety with him.
I use a NETI pot and have never had a reaction like you speak of, even when I was first learning to use it and ended up with a great deal of it in my stomach rather than my sinuses.
I wish you the best and hope you'll keep us informed as to how you're doing.
Peace
Greenlydia