I have an insect bite that looks like a bruise with a red dot in the middle. Should I be worried?

Watch. Watch it for signs of infection with increasing redness and swelling. Watch it for worsening skin darkening or skin ulceration, which can be a sign of a brown recluse spider bite. Do you know what bit you? Depending on where you live, lime disease or other transmitted disease could occur. Most of the time these resolve in a few days. See your doctor if you develop an illness or other concern.
Depends. It is possible that the bite could be caused by a recluse spider type due to the central red area and surrounding bruising (blue area). Have it seen by you primary physician.