I've always had allergies. When I was younger I sneezed, eyes watered, etc. Now I just get sinus headaches and neck stiffness. Anyways, I get sinus headaches pretty regularly, and they usually don't get the best of me. But about a month ago a friend gave me his cat. I had no trouble at first. The last couple of weeks whenever I am at home for a long period of time I get a sinus headache that lasts all weekend, till the work week starts back up on Monday. So basically my whole weekend is a headache. The thing is I don't know if it is the cat or something else, like a plant outside blooming, seasonal changes, etc. I clean the house regularly and I have a HEPA filter in the A/C. I guess there is only one way to find out is to get rid of the cat,but that is too drastic.

Be tested for cat allergy.

Sounds like you are allergic to your cat. I got a cat three years ago and the longer I had the cat, the sicker I got. I finally went to an allergist who confirmed my allergy to cats (I was in big time denial before that). One of the things the specialist suggested was to wash the cat with a product called OUTRIGHT. It comes in a spray or liquid that you rub onto the cat, then towel off. It's simple and seems to be effective. There are other simular products on the market too. I got the cat wash at a pet store. I hope you look into this, because if you are allergic, you will probably get sicker as time goes by. I love my cat too and couldn't part with it. An air purifier would also help.
Best wishes, SaraLee