No, don't loosen the bleed screw.
Did you remove both pads, then try to push back the piston? If so, this will some times cause the piston opposite to the one you are compressing to push out past the seal which will lock it in place.
The correct procedure is to pull out one pad, push it's piston back with a screwdriver, put in the new pad, then repeat the procedure for the other pad. In other words replace one pad at a time.
It sounds like you have caused a piston to push out past it's seal. When this happens, it's as if the piston is welded in place.
The cure is to either rebuild the caliper or replace it.
If you are replacing the pads one at a time and you still have this problem, I expect that it is caliper rebuild time.