Hair Thinning due to taking a GLP1

Good morning, I have been experiencing hair thinning, due to my medication, (Wegovy). That is the most likely culprit, but honestly it could be the PMOS(the disorder formerly known as PCOS), or the thyroid issues I have.

Either way, my doctor told me to use topical minoxidil. However big issue for me is how it makes my hair look and feel dirty. I tried the foam, and now I am trying a serum (Rogain), but both make me feel like my hair looks greasy all the time, unless I wash my hair everyday, which I am hoping to avoid. I currently am using a dry shampoo, to help, but by the time I get to wash day, it’s so weighted down, that it just looks gross.

Has anyone else had this same experience? What worked for you?