My cat just clawed at my nipple through my shirt and it hurts. Should I just leave it alone?

Clean it, then put some antibiotic ointment on it.
Remember, those claws also scratch around in a box full of kitty litter, urine and poo.

Need to wash the scratch with soap and water and then apply some antibiotic ointment regularly until it heals. Cat claw scratches can cause some serious infections sometimes. Not a place you want an infection.

clean the wound and keep it clean

Yes.