Our Shower fawcet has 4 screws that would allow the unit to be repalced, I am guessing yours does not. Are you sure the shower head line is tight. I know when we put a new shower head on that it tried to leak there. You might also look and replace the washer there as that might help as well.
You might post a picture and that might help some of us. If it will not let you post a picture that means you have to have 2 posts or more to the forums before it will let you post pictures.
Hope you get it fixed.
John