I tried the cool vest but it made me feel worse/strange and didn't really work for me.
However, I do get good relief from a cool neck scarf/bandana. It's filled with little beads that absorb water. You soak the scarf in cool water, wait for it to swell up, then tie it around your neck. It's easy to carry, easy to soak, etc. The little beads make it stay wet for much longer than a regular neckerchief. You can find them online. They're cheap, might as well order several for all you and your family.
Of course a broad brimmed hat and wraparound sunglasses are essential for light sensitivity.
Carry a good supply of sea salt with you. Mix a couple pinches (1/4 to 1/2 tsp) in with any water you drink (or just make it pleasantly salty.) Any kind of salt will work in a pinch if you don't have sea salt.
Try whatever you decide to do out at home first if possible.
For the long term, it sounds like you have both methylation problems and adrenal problems, and that these would be good areas to treat.
I've been able to eliminate about 90% of my MCS with methylation treatment. I've also been able to tolerate heat better and start being able to sweat from preliminary adrenal treatment. I don't really have POTS (or it's very mild), but those kinds of issues are also related to adrenals. The mild POTS type of symptoms that I had are improved.
If you get to a place with an air freshener, remove it from your room first thing and let the place air out.
Good luck!