Recently I had a new water heater installed by professional plumbers . I noticed a little rust in the water initially. My kitchen sink hot water tap is running cold water. My utility sink is running cold water at the hot water tap. My bathroom hot water taps work good.

Someone suggested rust in my pipes (50 years old) may have broken loose when the system was drained and clogged the valves.

Any suggestions or remedies?

Has this been an issue ever since the new water heater was installed? If so, call back the installing plumbing company and demand they come back to check the piping at or near the water heater. Sounds like some pipes got criss crossed during the heater install. Im not saying they reversed hot and cold at the water heater, but may have had to cut some other feed pipes to fit the new heater and got them mixed up. If this is indeed the issue, there should be absolutely no charge to you for them to come back and correct the piping issue.