I just got over a real bad cold and cough and im not coughing anymore but the left side of my throat hurts and it also hurts to swallow?

See your doctor. If there is persistent pain in your throat and pain with swallowing, see your doctor. If she can't take care of it, you may need to see an ENT doctor. Your problem can't be diagnosed without an examination. Other conditions, such as a peritonsillar abscess, will need to be ruled out.
Residual... This could represent residual throat irritation from the cough that was present with your cold symptoms. If this is the case, the throat irritation should improve over the next few days now that the cough has resolved. If you do not notice any improvement, see your doctor to determine if there is something else going on. If you smoke, now is a good time to quit to decrease inflammation.

Related Questions

I have a common cold with cough, sore throat and mucus, does it get worse after 2 days?

Cold. Not sure of the question. Sounds like a viral illness in which symptoms don't always develop all at the same time and typically don't all resolve at the same time. Symptoms can last for up to 14 days and sometimes cough lingers for even longer- can be with or without mucus. Read more...