If both cold and hot water run equally bad, that means not the faucet, but the shower switch is clogged, especially if its rotary and non-automatic.
To start cleansing, unscrew the switch assembly.
Remove the sealing ring. Scrub away all visible rust with a brush or a nail.
Pour in any anti limestone and rust liquid you have. If you don’t,
a strong citric acid in boiling water mixture will do.
Leave gor a hour, pouring more if needed.
Now run some water, using the output as intake.
Reattach the switch. The water should run fine now.