You have a cross-over somewhere...it could be at the washing machine's connections, or some single handle faucets when they get worn can allow hot and cold to cross-over. Some brands are more notorious for that than others. To narrow it down, one by one, shut the cold water supply at each faucet in the apartment. WHen you find the one that stops the cross-over, you'll know which one needs to be repaired or replaced. Some single handle faucets will allow you to have the water turned off with it turned all the way to one side. Some force the handle back to the center point. If you can turn it all the way to one side, you might be able to try that rather than using the shutoff under the sink. If there's more than one tub/shower valve, those often don't have a shutoff, so then it becomes harder. Can you tell what brand faucets and valves are there?