The tip of my right index finger appears to be infected. it's puffy, painful and red. are antibiotics always appropriate and if so, what type?

Difficult to know: Antibiotics are not always needed. You may have a felon - which is an infection of the pulp - or a paronychia - an infection of the nail base/edge. Alternatively, herpes whitlow can present with these findings (if recent herpes simplex oral ulcer). If the swelling/redness is primarily along edge of nail, you could use a file and lift the nail up from the side - and soak. See a MD.