You could go to urgent care for the cold but really it would just be a waste of time and money.
Most colds are just a viral cold that require time to get rid of and they usually go away within a few weeks at most.
So what the urgent care center would do is recommend you get plenty of rest, stay hydrated etc and then wait a week or 10 days and the cold should be over.
If the cold lasts longer than 10 days then you might want to go to urgent care to make sure it's nothing worse such as turning into pneumonia but most times the cold will go away within 10 days but sometimes might last as long as 14 days.