Drastic change of climate makes my hair fall out: what tips do you recommend?

Hi all!

I moved from France to Polynesia six months ago. Between the huge amount of stress, the drastic climate (hot + humid) and the hard water, my hair is falling out, which I kind of expected, but still. Doc put me on supplements a month ago (biotin,zinc, iron etc), I switched to a mild shampoo and I know patience is probably key but is there anything more I can do?

I've been noticing teeny tiny regrowth that is thin and fragile. Also, my sclap seems to retain some buildup (Im thinking it's from sweating a lot, I'm really not used to hot climates).

I have medium length wavy (2b?) hair.