I have been feeling sick for a week and I have a foul smell in my nose that is worse when I sniff or try to blow my nose. I can also taste it in my mouth what is this?

It is foolish and dangerous to diagnose over the Internet - it could be anything from a sinus infection to an infected tooth and just about anything else.

You need to see a Physician and possibly need to go on a form of antibiotic. A week is a long time to be sick without medical intervention!