My Cat Bite Me Approximately 3 Inches Above My Wrist

my cat bite me approximately 3 inches above my wrist on my arm--3 puncture wounds. I immediately flushed and washed with soap, then applied ointment. It is now swollen slightly in an 1/2 dollar size area..pain above wound approximately 4 inches up arm and into nuckle area. No redness, wound looks good not open more healed looking. Just very painful. My cat has all her shots and sees a vet regularly.