If your hair is falling out in clumps resulting in bald patches, perhaps you have alopecia? Might be worth a visit to a dermatologist to determine. If it's generalized, diffuse hair loss, telegen effluvium, that can be brought on by stress and usually resolves. It it's alopecia, that's an autoimmune disorder resulting in small round patches of loss (alopecia areata) or total baldness (alopecia totalis). Hair loss after Covid is quite common. A dermatologist will be able to diagnose and will hopefully order bloodwork to see if your thyroid is functioning properly as hypothyroidism can cause hair loss. They might also check iron/ferritin levels. You might consider working on stress reduction (almost impossible when you are losing your hair. I know from experience!) and also making sure you are getting proper daily nutrition. Adequate protein is really important as well. I was diagnosed almost 20 years ago with alopecia and it was my hairdresser that discovered it as well! I treated it medically for many years which was a mistake but the only option at the time as there wasn't a dietary understanding and integrative approach that I could find. Many years later information became available on the association of gluten and autoimmunity. I ended up eliminating gluten and dairy entirely and the condition mostly resolved. If it ends up being alopecia, feel free to message me if you want to discuss.

Hair loss wasn't signaled in the clinical trials. Nonetheless: "Other research shows parathyroid hormone (PTH) may impact hair follicle growth. PTH regulates calcium in the body
Thinning hair is also a symptom of HPT. "
Forteo is parathyroid hormone. It floods your bloodstream briefly and could be affecting hair loss. There are scattered reports from patients suggesting this side effect.
Weight gain is another side effect unsignaled in the clinical trials, but widely reported in patient sites like this one. Especially belly fat.
You might want your physician to order CTX, and P1NP to acertain that the drug is still working to your advantage. The fingernails make me suspect that you might want to go on a bisphosphonate for a couple of months before resuming Forteo.