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.

When your dentist goes in and removes the decay from your tooth, it is very painful and can traumatize the tooth.  Luckily, due to the anesthetic, you usually don’t feel the pain caused by this process of repairing your tooth what is the main cause of tooth sensitivity after a filling because your body is telling you that the tooth was traumatized. 
The bigger your cavity (and resulting filling), the more likely it is that you will experience sensitivity after the filling is done depending on the different cains of rehabilitations. There should be no pain after a restoration and you might had a trauma and will need a root canal. With xrays we can determinate the root condition and what other options we can have for the tooth.