I think with SLE the rash on your face would be more prominent, than any other. It does sound like you are having an allergic reaction to the sun, when you talk about arms and legs. You can test that theory... go into the sun without any protection and see if those exposed areas are where the rash is worst?
There are STIs that act this way, esp from a sore/eye and once touched go throughout the body... I would think the doctors would have ruled that out already? And measles...
HOW about poison ivy/oak/sumac ??? It's a rash that takes effort to erradicate, and it will flare in sun. Because it's base is an oil, if you touch anything someone else had touched (they having been into the poison ivy) it will transfer... Does using product for poison ivy help with the rash?
Have you used oatmeal baths to cut the itching down? Or aveeno. Same thing.
TC