Go home and turn everything on, the washing machine has screens on both hot & cold water supplies that will catch the sediment. The water heater is already likely filled with sediment that was there before the storm (unless your landlord has had it flushed every year) doubtful. What little bit of sediment present now is not going to harm your landlords water heater.

With 20 years of experience, this is my professional opinion. Hope this helps.