I have a single knob on my bath tub that controls the hot and cold water. When you rotate the knob a half way it is cold water and a full way it is hot water. The cold water comes out, but the hot water does not, just a drizzle. I removed the faucet and found there is one pipe coming out of the wall and connects to the faucet. When I rotate the knob to control hot or cold water, this pipe rotates. Inside the wall connects to this pipe are a cross-shape pipe. The upward probably goes to the shower head. I wonder if the leftward and rightward are the sources for hot and cold water. Since there is no hot water and only cold water, does it mean the pipe for the hot wafer side is clogged? Do I have to break the wall to check the pipes? Please help!

(p.s. it is a house I just bought and I never used that bath tub before)