Is it normal for itching and redness to persist after a full course of antibiotics for cellulitis caused by staph?

Yes, it can happen: Staph infections can cause all kinds of problems for your skin. Even after finishing a course of medication, your lymphatic system may be damaged or may be draining away the damaged tissue from the site of infection. It would be worthwhile to keep in close contact with your physician for areas that do not continue to improve after stopping the antibiotic therapy; you may need a 2nd course.

Possible: It is possible for skin to stay slightly red and itchy as inflammation resolves. That being said, if you haven't noticed much improvement over the course of the treatment, then you may want to be re-evaluated. It is possible that either its not cellulitis or you aren't taking an antibiotic that is effective against your infection.

Can be normal: Sometimes the area of skin overlying an infection can be itchy for a while after the infection is gone.

Persistent swelling: Lymphedema which is sudden swelling of skin is the cause of itching - skin is stretched suddenly beyond its elasticity to alleviate this apply calamine lotion to skin. Fill old long socks or stockings with packaging popcorn styrofoam peanuts and tie the socks/stocking use this padding one on top of leg another on calf side and use acewrap apply this in the morning remove at night. Itching will go.