What would cause a skin rash? It does not itch, but is spreading. I don't recall using any new soaps, lotions, detergents, medicines, etc.

Too many things. Too many possibilities to answer here in such short space. As you said, you haven't had any contact with things that could be a cause so you should get the rash looked at by your doctor.
Many things. Rashes can be caused by many different types of things such as exposure or illness. In order to determine what is causing your rash you need to be seen by a doctor. Rashes need to be seen in order to try to diagnose and treat them effectively.