My mother had a bleeding ulcer a few months ago and the doc told her no more alive. She has a sinus headache that has not gone away with Tylenol is there something she could take that will not upset an ulcer if it is still there?

She needs to consult with that same doctor. He knows her history; we don't.

You mean Aleve. I agree, this is a question for her doctor. Perhaps an anti-histamine?
She needs a referral to a allergist and A DENTIST!!! Speaking as one whose sinus problems are related to dental problems. Many are allergy related. A few, if of long duration, can be bacterial infection.