Unknown illness haunt my girlfriend for nearly 20 years

My girlfriend (27F) has a unknown and rare illness for almost 20 years. She has pretty much already given up on any cure but I would like to know if reddit can at least give me a little direction.

Her problem is that she cannot sweat. More accurately, she cannot regulate her body temperature by using sweat. Because we live in south-east Asia and the summer here is no joke, her life is pretty much like a vampire that live in an air-conditioned apartment. If she really need to go outside, air-conditioned interior and taxi is a MUST.

No sweat means no exercise at all. She cannot walk under sunlight (a walk at night is fine but not for too long). So her health is quite bad. She is now 70 something kilograms (154lbs) and she is about 160cm (5 feet 2). She is kind of obese and this make her body temperature regulation even worst.

Here are some observation I have about her illness:

  1. She CAN sweat. It's just that she cannot sweat more when needed. And she did visit doctor and have a sweat glands check. Doctor said her sweat glands are completely fine (Not sure what is the name of the check).
  2. Apparently, her menstruation affect how much she sweats. She said before menstruation she cannot sweat at all which make her feel incredibly bad but after menstruation, she sweat more. So she feel better about menstruation and can even take a 10min daytime walk.
  3. She has oily face. So that probably means there is no problem with producing oil or grease like we do.
  4. She has headache very very regularly. I know it is likely caused by hyperthermia but sometime she had headache even though she does not feel hot at all.
  5. Her body clock is very messy. Every menstruation delays at least two days compare with her previous one. She often sleep at 5am and wake up at 3pm and the sleep time and wake up time is everchanging.
  6. Her illness start when she was 10. At the beginning, it is just once every month so everyone was thinking it is just a topical bad day. However, it got worse year by year and when she was about 16. She has to stay in air-conditioned room at the time.
  7. Her skin DOES NOT have any apparent problem. No weird color, no weird spot. It is just a bit dry. The only thing stands out about her skin is her hand. Her hand's texture is very rough.
  8. She said that this illness probably is a psychological problem originated from her parents divorce because the divorce and this illness happens in the same year.
  9. Her family (two generation up. From parents to grandparents) has no such illness. She had a 4 years old boy but he does not have such illness either (At least for now).

This is all I observed. If you have any idea what this is. Tell me in the comment. I will read through all of them just to have some hints of what this illness is. Thank you!