I've had a cold with a productive and raspy cough followed now with lots of sinus pressure and congestion for over 3 weeks. Sinus infection? See a dr?

See a doc. Because this is going on for so long, it's worthwhile to get checked. Antibiotics are rarely needed for bronchitis or sinusitis, but when symptoms persist for over 2 weeks, especially if they are getting worse... Sometimes antibiotics are what you need. Your doctor will be able to help you out with this one.
Possibilities... Your symptoms could all be due to an infection, probably viral. But, your symptoms could also be due to allergy, especially with the duration of your symptoms. You need to see your doctor to be diagnosed so you can be properly treated.