Same here! Didn't lose much weight, mostly just hair, mine's long and fine but there's tons of it, shedding in brush-fuls just like yours, all over the pillow each morning, genuinely afraid to shampoo it or comb through it, kicked off around 3-4 months in.
Bloodwork before Mounjaro was all normal. Six months later, everything fine except low zinc, retested and got the same result.
Honestly think Mounjaro pushes you toward being way more intentional about food, since the noise disappears you plan meals ahead rather than eating out of hunger. Point is, I was probably being extra careful getting a good spread of nutrients, so doubt diet caused the low zinc.
Doctor prescribed a strong zinc dose, roughly triple the RDA, for two months, then said to just watch my regular multivitamin covered it after. That was last fall, took until about a month ago before my hair felt normal again.
Might tie to that seven-month hair cycle people mention, but you get through it.