Here's the kicker. I replaced the galvanized pipe from the basement to
the second floor where the bathroom is. Actually I had someone do it
for me. I didn't go across to the tub because when the house was built
the pipes were imbedded into the mortor of the bathroom floor. I
figured if I tried to remove them I'd lose the floor. At the time
water pressure wasn't an issue. I kind of think I'm stuck.

wrote:
I just had a similar issue with the hot water in the bathroom sink.
Shower was OK. I messed around for a few hours trying to backflush the
galvanized pipe, replaced the 4" nipple that collapsed from rust, etc.
I ended up having to replace the pipe back to the water heater with
copper. This was a 1950s vintage house and you could not see light
through a 4" section of pipe it was so corroded.

It is probably the galvanized. If you have already checked the faucet
and other easy things, it is probably time to replace some pipe,
especially at 80 years old.