It is not out of the ordinary to have a sore throat following a cold. Drainage from the cold can make your throat feel raw. Are you having trouble swallowing? Is it getting progressively worse, or better?
It's not possible to diagnose over the internet from a picture, but the two most common illnesses that would cause a sore throat are strep throat (bacterial) or enterovirus (virus). Strep throat may require antibiotics in order to cure, but unfortunately, like most viruses, enterovirus must run its course. A doctor can prescribe low-dose steroids to alleviate the pain and swelling, if needed.
Hello~If your current physician isn't helping, I would certainly see another one. You need to probably be on an antibiotic if it is a strep throat as it can lead to something more serious.