Public Service Announcement: Don't Bite Your Friends
Human bites may be more dangerous than most animal bites. There are germs in some human mouths that can cause hard to treat infections. If you have an infected human bite, especially on the hand, you may need to be admitted to the hospital to receive antibiotics through a vein (intravenously). In some cases, surgery may be needed. -Medline Plus/NIH.gov
Personally I'd have reserved judgment on saying "I'm okay now" until getting checked for rabies or having my arm surgically removed.