Replace cartridge of valve for shower
Looks like you have shut off valves built in (second picture) the flat head screws on either side of the lower handle. you can shut them off and remove the cartridge to take it to a plumbing supply and they should be able to tell you. 

Looking at the 2nd photo, it appears that the hot side is shut off or at least partially shut off. Try opening the valve and see if that helps.