For my recruitment, we weren't allowed to have anything with us when visiting sororities or between rounds. Our stuff was locked in a room/supervised by Gamma Chis, so you only brought the minimum- Phone, Room key and ID, and they stayed there for the duration of your parties.
We got panhellenic issued pin-on nametags, and I hid some advil and bandaids in mine for pref
But honestly I think it was better not to have all of that stuff to fuss with, by the end of the night nobody's hair was perfect and nobody cared. It was pointless to worry about your makeup, there was nothing you could do about it and mirrors were covered anyway.