My boy also got a cough a while back. We waited for a week and it didn't subside so we brought him to see the pediatrician. I wouldn't recommend a GP unless you know that the GP is competent in treating babies.
The pediatrician prescribed me Zyrtec and Rhinathiol. The first was for his running/blocked nose and the other for his cough. It subsided for a week and then it came back again on and off.
After a month, he was still coughing so we brought him back to the pediatrician. This time he gave antibiotics coz he was already having quite a bad sorethroat from all the coughing. He also prescribed two other meds for him and that cured him completely.
For our son, the cause of cough was from infant care.
If you're sure that your baby has caught a virus, it's best to see a doc. My pediatrician also advised us to hydrate him and keep him warm. He even asked us to stop feeding solids for a while and go on full milk. I think it's so that his body can pass out the bad stuff from his urine which is also the logic why adults need to drink water when ill.