Had a filling. Cold water still bothers it after months?

There is often tooth sensitivity after a filling, however it should subside within a few weeks. Possible reasons for this are: You need a root canal or you have a leaking filling - best to head back to the dentist and get another x-ray. This should ascertain what the problem is.

it is common to have some sensitivity for a week or two after a deep filling. If it has not improved after that you have irreversible nerve damage and will need a rootcanal 

Having tooth sensitivity after the filling is very much obvious because a tooth that has just had a filling placed will be more sensitive to hot and cold foods, air temperature, and the pressure of biting but it could be resolve within few weeks. In case you are still having senstivity issue after two week and does not decrease then it's the time to contact dentist.