Hi Frangipanis:
If the shower head is DRIPPING when you shut the valve off then the problem will be at the washers associated with the shower valve.
Basically, you will need to shut off the water to the house and then remove the chrome trim and handle(s) and remove the cartridge assembly/washers and bring them to a local plumbing supply house or home depot and get a replacement.
Not a real hard job, but definitely need basic mechanical skills...
If you can provide us with a NAME on the valve or post a picture of the valve we should be able to tell you more here...
MARK
PS: How many handles associated with the valve...one, two or three?
.