Inflamation on right side of arm like a red circle that is swallen and hurts when contracting arm. it looks like a sting from an animal. what is that?

Sounds infected: though I can't see it, it is most likely a cellulitis or abscess. These are forms of infection of the skin tissues. Go get it checked out. It could be other things as well, but it's worth getting a medical eye on it.

See your doctor: You may need to be screened for Lyme disease. If it is a tick bite or it may just be an allergic dermatitis but the only way to know is to see a doctor. go ahead and take a pictureof it now to show your doctor when you get there. that way if it changes she will be able to see the progression.