I had strep throat a month ago and developed a rash all over my legs and arms. It is itchy and seems to be getting worse. What could it be?

Rash with Strep. It sounds as if you may have developed guttate psoriasis which commonly presents after a strep infection. There are other conditions, such as syphilis, which also present with sore throat and a rash. Be sure to get evaluated by a doctor, preferably a dermatologist, who will be familiar with the differential diagnosis.
New Infection?? Is this a new rash or left over from the old. If new, it could be strep. It could be eczema. There are too many unknowns here. Need to discuss with your doctor.