@januaryjane- It's nice to meet you. Were you born in January? 🙂 Erythromelalgia is a very rare disease. I've never heard the name but I have heard some people complain about some of the symptoms. I found this on the Nationa Organization for Rare Disease's website so you can learn about it.
Erythromelalgia is a rare condition that primarily affects the feet and, less commonly, the hands (extremities). It is characterized by intense, burning pain of affected extremities, severe redness (erythema), and increased skin temperature that may be episodic or almost continuous in nature.
https://rarediseases.org/rare-diseases/erythromelalgia/
What symptoms do you have that might lead you to think that you might have Erythromelalgia? I'm not sure that you are talking about feeling ill or burning. If you feel ill in the sun, and it's not about burning then I would recommend looking through all of your medications to see if they make you sun sensitive. I was on the beach a while ago with a friend. She had been warned against lying in the sun because she was on an antibiotic that made her sun-sensitive, not only to burning but also to feeling ill. She wound up having to leave the beach and go to her doctor. I would also recommend turning the AC up high to cool the car. I would also make sure that you are well hydrated.

If burning is your problem than I use EltaMD and Tinosorb. I get the tinted ones (I'm an older gal who loves to have even-toned skin. Both work beautifully. But you must re-apply it throughout the day. Sunblocks do not last all day no matter if they are waterproof! There are also lightweight sun-protecting clothing that works. Surfers use them. Just google sun protecting clothing and google will show you a whole bunch of stores that carry them. And it's Memorial Day weekend so there are fabulous sales!

Have you spoken with your doctor?