I've had a really bad cough for 3+ weeks now then couldnt swallow went to docs diagnosed tonsillitis they gave me penicillin but now its worse.?

Alot worse?: If worse it needs to be checked. If you develop trouble swallowing to the point of drooling, painful opening of mouth, tender lymph node in neck opposite tonsil, you could have a peritonsillar abscess. If it's the cough that's worse, so long as you're not coughing up green or yellow, it's likely viral and will pass. If coughing until vomiting, may have pertussis, and need different antibiotic.

May not be tonsils: Tonsillitis usually won't give you a cough. A sinus infection can give you a cough and a very bad sore throat. Penicillin although a good drug for tonsillitis is a very bad drug for sinusitis. Consider going back to your doctor again and telling him or her that you are no better. Have them examine you, listening to your lungs and see if they think an antibiotic for your sinuses would be better.