Does this happen to every fixture? Take one apart and look for debris on the filter screen. In a water heater the cold water enters and is piped to the bottom of the tank through what is called a dip tube. Sometimes, this plastic pipe will dissolve into very small pieces -pencil tip size, which get into the downstream pipes and ultimately will clog similar to what you are describing. Also, check your shower valve cartridge for this clogging too. If this is the case, a new Wh, and flush lines and clean each fixture filter screen will do the job.
