Your daughter's doctors might want to consider the relatively uncommon diagnosis of sunlight angioedema. A related condition, sunlight urticaria, has been associated with another rare condition, porphyria. Your daughter's illness doesn't suggest urticaria, commonly called hives, as itching is almost always a symptom with that. A more general suggestion would be that any and all diseases, especially those that present with fever and abdominal pain, that are associated with photosensitivity to sunlight be considered in the differential diagnosis. A dermatologist with sub-specialization in diseases worsened by exposure to sunlight, would be a good starting point.
Good luck.
Im not a doctor but I have a son has lots of different issues and one of them is similar to yours. When he gets hot he turns red his feet swell and he has siezures but he is epileptic though so don't worry about that part. He also has very visibly veins in his chest when hot and sometimes gets a rash. I was told by specialist that its a sensitivity to heat ( can cuase heat rash) and may be a allergic reaction to the sun. I suggest keeping her cool as and shaded and make sure to have cold water on hand at all times. When you find a tap refill a water bottle with cold water if it got warm if you know she will get hot. Cold drinks work well to like slushy. I also sometimes put water on my sons hat and hair allot if we are out in the sun or if theres no ac. It has helped him I hope it will help you feel at ease and your daughter. Keep cool : )
The rash she gets is on her cheeks of her face. The only test that always comes back with anything is her blood test that shows she has inflammation in her blood. She did develop last year benign rolandic epilepsy but has not had any in a long time. The fevers she gets are any where from 103 to 105. There is no pattern to them other then she tends to get sick after being in the sun, being active and being hot.
Sorry I forgot to add it might be safe to have benidryl on hand if the swelling gets to bad, and contact your doctor if your still aprehensive.