Since the shower head has no effect, I would suspect the valve (faucet) itself is the problem. If it's a known brand it can be rebuilt. Or just replace it. In most cases a standard shower valve from Home Depot or Lowes will work.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC