If there’s no cold water in your shower but cold water comes out of every other faucet just fine, then the problem lies in the shower faucet cartridge.
This cartridge contains a pressure balancing valve that sometimes fails, thus preventing cold water from flowing out of the shower head.
Removing and replacing the cartridge should fix the problem. Sometimes a special tool called a cartridge puller is required, in which case it might be more convenient to call a plumber.
