What would cause rusty water coming from hot water faucet?
One reason for this can be the water heater. If it is more than a few years old you may have rust or sediment that has accumulated in the bottom of it. Water heaters have a valve near the bottom. Those are supposed to be used to flush out the sediment/rust from time to time. Most people simply ignore them. Unfortunately this allows the sediment to build up causing problems like what you have. Not only that but sediment build up in the water hot water tank can drastically shorten the life of the water heater. If you should need to replace your water heater, buy a good one. Something like an A.O. Smith or similar will give you good value for your money. It is well worth the price.