There are many rashes and spots which will go away of you ignore them. Your rash is not one of them.
You may be right that this is "ringworm"--fungus. Or it may be eczema of some sort.
Here's my advice: Make an appointment with a doctor. Then while you're waiting for the appointment, go to the drugstore and get some clotrimazole 1% antifungal cream (non-prescription)and put it on twice a day till you see the doctor. That will help clarify the situtation and may help the rash too.
Fungus, by the way, is often not very contagious, despite its reputation. If no one around you (roommate, sexula partner) has it, that wouldn't be surprising. If they do, see a doctor faster.
Best.
Dr. Rockoff