your movement is "wrong" in some way in that you are placing undue strain on a certain part of the playing apparatus in the more difficult sections..
Yes there is a way to practice without feeling the ache/pain, there is however no way that I can tell you what exactly you need to do to resolve it without watching you play, there are too many potential causes and variables. Really though, your teacher should be able to help you.. not just say "no it shouldn't hurt".
Since you are working on la campanella it seems likely that you have some technical problem that has been built in for some time, its just showing itself now because the music is getting harder. Same with the chopin, the piece is designed to be very difficult to play comfortably to show you the flaws in your technique. You shouldnt bang your way through it. Figure out whats going wrong. With a better technique, not only will it stop hurting, but you will obviously be able to play it better aswell.