How do I stop being covered in tiny hairs?

I don't remember having this problem six years ago, but I swear that every time I get a haircut, I have a bunch of tiny hairs stuck to my neck and face. Yesterday, an employee even stopped me on my way out to try and wipe the back of my neck off. I still ended up in the bathroom, trying to get even more off my neck and face before heading home.

I've been living somewhere with kinda high humidity and hot, so I keep thinking it's a me problem. Maybe my skin is just too damp?

Do I need to ask for a towel between me and the cape? Cover myself in baby powder beforehand so my skin is drier? Am I alone with this problem?