I got a new inner tube for my bike and it's way bigger than the rim, It's just its usual size; didn't inflate it too much or anything like that. The older one I was replacing just fits fine. IS this too big and what side effects can this cause ?
Some tubes are just like this. It is unlikely to be a problem in use.
Put a bare minimum of air into it - just enough to handle it, but not even the amount that fills out its base shape. From there, insert it into the tire. You will probably find that it also wants to be a little bit bigger than the tire. Distribute it all the way around so it's not kinked or folded onto itself anywhere. I usually kind of pluck and nudge it into place to do this.
If it does want to fold over onto itself no matter what you do, and you have to make it work, put some talc powder (or baby powder) in a ziploc bag along with the tube and thoroughly shake to coat, then reinstall it and pump it up. The talc helps it automatically distribute itself around evenly under pressure.