I had the opposite problem. After one Prolia injection, my hair was coming out in clumps. It was freaking me out. With Evenity, thankfully, I haven't noticed any hair loss.
Are you having bone turnover marker tests to be sure Evenity's working for you? Most people have great results, though I've read a few stories on here ehere that wasn't the case. I can't imagine you'd want to lose your hair to then find out it didn't work. If it IS being effective, you may decide it's worth investing in that wig.