The Wild Ewt of the Plains of Canada

If you keep running the hot water does it eventually run clear?

I've had random rust turn up in things that have been unused for a while but that clear up if you run the water for a while.

I'd run both taps to see if rust is just in the hot.

It might just clear up, but I suspect not.

If its a 'constant hot water' system then it might actually be the water company rather than your boiler.