leak in pipe behind showerhead. I'll bet the leak is in the supply pipe. And, lucky you, that pipe is touching a stud in the wall so the water slides over to the wall instead of all falling down inside the wall to the basement.
If the drain leaked, you would see that as a wet spot on the ceiling of the "lower level" as water falls down under the force of gravity. Very little water would slide sideways over to the adjacent wall, and virtually none would get past the wall's sheetrock to soak into the carpet.
Try only cold, and then only hot water in the shower. Five minutes of cold, turn it off, wait an hour. Five minutes of hot, wait an hour. You can also put a stopper on the tub drain so that water doesn't drain out, just to separate the possibilities.
David
edit: you can turn the hot water off 100% at the valve at the hot water heater, to be sure you are only getting cold water when you want cold water at the shower head. In case your mixing valve doesn't shut off 100% of hot and cold.
Then, when you have seen that the problem is one of the supply pipes, or both, you will know whether the problem is in the pipe below the shower mixing valve or right at the connection point to the shower mixing valve. Also, this will confirm that it's not the drain.