I got a very bad cold and was on antibiotics for three weeks and now my mouth is so painful. ?

Paimful mouth: Being on antibiotics for 3 weeks is a long time and you are probably dealing with oral candidiasis which is a fungus overgrowth since the antibiotics killed your normal bacteria. There are good treatments for this ---mycostatins, liquid or tabs.

Several answers-: 1. Pain is from ulcers caused by a virus (cold sore) or fungi (thrush) that is not covered whatsoever by antibiotic; 2. You are experiencing a drug reaction (peeling of tissue in mouth- a stevens johnson reaction); 3. Bacterial resistance to the abx used; 4. Source control not achieved (eg. Abscess); 5. Diagnosis is something other than an infection. Consider an id or ENT specialist consult!