Transportation of a pet fish. Via airplane. How does that work out? Help, i guess. ?

This summer i intend on moving to an almost neighboring state and i plan to fly solo. I have a pet fish that i want to take and i'm worried of how he will be transported during the whole airplane ride dealio. Will they allow me to carry him with me and be up with me where i sit on the plane or must i put him in some kind of "carrying bowl" and have him packed away in storage. How does that work out? I really don't want to leave my fish behind.
Erh. I'm not sure exactly how to get in contact with an airline. I'm trying to search things up at this very moment.