I just had my water heater replaced, and am getting hot water downstairs in the kitchen, but not in the bathroom upstairs. All I get is a very small stream of cold water coming from all the hot water taps. :confused:

What has happened is that in installing the water heater you have disturbed some mineral built up in the pipe walls and it got sucked up into the faucets in the bathroom where it's now clogging the faucets.
The solution would be to shut the water off to the valves affected and open them up to check and clean the hot water inlet ports on the cartridges. Before you button them back up Turn the hot water back on for a minute to flush out the branch and supplies. Good luck, Tom