If you just have a common cold then going to the doctor for the cold would be a waste of time and a waste of money as well.
There's no cure for the common cold and there's nothing that a doctor can give you other than tell you to stay hydrated, take some cold medicine, get plenty of rest and within a week or 10 days the cold virus should be gone.
Now if the cold gets worse then they might be able to do something about it but for the common cold there's no cure and you just have to let the cold virus run it's course.
I'm usually feeling better within a week and sometimes it takes up to 14 days for the cold virus to be fully gone depending on how severe the cold virus is that I have.
But there's not much if anything a doctor can do for the common cold.