Ticks carry many diseases, perhaps none so deadly and frightening as Lyme disease. One of the telltale signs that you might be infected is if the bite expands, with another red circle appearing around the original site of the bite. This gives the bite the appearance of a red bull's-eye, though this doesn’t have to be present in order for Lyme disease to occur. Seek immediate medical attention if you develop a bull's-eye around your tick bite.