First of all, Depot-Provera is NOT progesterone. It's a progestin with progestogenic properties but with also very different properties than progesterone. Contrary to progesterone, it exerts mild androgenic effects which could explain the hair shedding, it increases DVT and breast cancer risks, tends to oppose estrogen's beneficial effects on lipids (i.e. HDL) and may cause depression/irritability/anxiety in some. It is not used in women who are pregnant to prevent miscarriage due to its androgenic potential whereas progesterone IS used because it has no androgenic effects.
It does have strong anti-androgenic effects as far as suppressing the pituitary gland's LH production and thus testicles's production of androgens BUT if you are already taking Spiro and estrogen and a DHT blocker that all inhibit androgen, then the addition of Provera, is, IMHO, not necessary.
You should raise these concerns with your doctor so that a proper course of action can be put into place to remedy the situation.