Do you actually feel like you have a cold (headache, body aches, fever etc) or is it just a runny nose? You may have rhinitis (which means runny nose). I had this last year, started with a cold, after a few days I felt better but nose kept running and I coughed up phlegm for weeks. A nasal spray (steroid, not decongestant) from the doctor got it under control.
If the doctor insists you need more antibiotics, ask to have a sample tested first to see what infection you have, so you can get the right antibotics for the specific infection (if you have one).