Doesn't sound like a spider bite. It could be dermatitis or ringworm. Ringworm can start out as a little red bump, where the fungus starts to grow, but then spreads out into a circular or ring-shaped lesion.
Dermatitis can be caused by many things, including reactions to bug bites, laundry detergent, and jewelry.
Ringworm is a fungus and can be spread person to person, animal to person, or animal to animal.
A picture of a typical ringworm infection (which by the way, can be cured with athlete's foot cream or spray):
http://en.wikipedia.org/wiki/Ringworm
A picture of contact dermatitis or allergic dermatitis:
(bugbite):
http://dermatlas.med.jhmi.edu/derm/IndexDi
splay.cfm?ImageID=-999087472
Contact irritant dermatitis:
http://dermatlas.med.jhmi.edu/derm/IndexDi
splay.cfm?ImageID=517862452
Contact allergic dermatitis:
http://dermatlas.med.jhmi.edu/derm/IndexDi
splay.cfm?ImageID=-1410187365
In order to tell if you have either ringworm or dermatitis, you need to see a doctor. If your lesion becomes swollen, oozes pus, gets bigger, or if you start to run a fever, make an appointment with your doctor asap, as an infection could be brewing. Not all dermatitis lesions look alike, and not all ringworm infections look alike, it is best that you see your doctor, who is better equipped as well as certified to diagnose and treat you.