If the cold water pressure is good, then you are right about the shower head not being the problem.
Check the hot water shut off valve feeding the tub to assure it is opened fully.
Also if you have good hot water pressure at the vanity and are sure shut off valve is fully open, the problem may be in the mixing valve that feeds the shower head. It's not uncommon for deposits to form over a number of years in this valve and restrict flow, especially on the hot side. Could also be a broken or stuck washer in the mixer. You can shut off the water to the valve, hot and cold, remove and inspect the cartridge from the front. Remove the handle(s), the bezel trim and the valve cartridge should come out with a wrench. If any of the internal parts look suspect, take it to your hardware store and they can help you select new soft parts to rebuild it. Replace it in opposite order that you disassembled it, and don't forget to put some plumbers putty under the top and sides (not very bottom) of the bezel, so water won't leak in behind it and down your wall.
Good luck.
Usually cases of a slowly decreasing amount of water are that a filter has become clogged. Does your water supply have sand particles coming through? Check the diverter heads for other faucets in the house. Are they getting many small particles trapped in them? Sand in one faucet tells you that all fixtures are getting clogged, some more slowly than others. This sandy junk can come through municipal water systems, or it can come from your own well if you are on one.
If you are getting much of this coming through, you may choose to install a whole house water filter to prevent that.
Whatever you find in those other faucets, if the problem is both the shower head and the tub spout, then the problem is in the fixture itself. Is this one of the new style fixtures that regulates the temperature of the water? I have read that those temperature regulators can sometimes be a problem themselves, improperly shutting down water flow.
If not that, assuming this is a cartridge based fixture, then you will need to pull the cartridge from the faucet. This entails removing the handle, then removing a locking nut that holds it together. Please shut off the water BEFORE you do any of this! The cartridge will come out, although this sometimes takes some amount of persuasion.
You can buy either a complete cartridge replacement from most manufacturers, or just a set of new o-rings etc., to rebuild the cartridge. Large home centers will have an entire wall filled with various such replacements. Bring in the old cartridge if possible to get a match. Knowing what company made your fixture will help.
A possibility is that a piece of rubber from an o-ring or other seal has cracked and become lodged in an orifice inside the cartridge. Look for this, or for other problems when you open up the cartridge.
Best Answer
Since you do have hot water coming out of other faucets it is most likely your shower valve.
Many of the single handle shower faucets have a cartridge valve that is very easy to replace. The cartridges are specific to the faucet so you will need to look up your model. I had a similar problem with mine. The cartridge cost around $60 and took about 10 minutes to replace.