There are many forms of travel. Boat, plane...your little second cousin. Papicka can't really walk, so for now Headlight has been carrying her from class to class. Headlight's Pikachus are now staying with Papicka for protection, surveillance and moral support.
Papicka is completely terrified of being hugged, cuddled, or picked up by 'mon she doesn't know, so naturally the PCA is a bit hard for her. Especially since she can't escape unwanted attention. Ever since a surprise hug from Karma caused Papicka to cry, Headlight has been ferrying her everywhere. The only time Headlight leaves her is during classes and while in the locker room (Headlight uses the boy's locker room, as she doesn't like girls in general) in the latter case, Papi is left in the care of the Pikachus and Mighty-anne.

And yes. Headlight's tail is really strong.