My iPhone 5C battery is going insane?

First of all, my phone looks burst. The back piece of my phone comes a bit out of the back cover. Then, when I charge my phone it changes by itself it might be 40% when I put it to the charger and while it's charging it goes down to 2% its driving me insane! Also, my battery dies so fast ( I haven't got local servises on nor push mail ). It sometimes turn offs even when the battery is in 25%. What should I do? If I take it to someone to change my battery, will it harm my usage? Will my stuff be deleted/gone?

Here is something you can try. Don't know or will say if it will work for you but could be worth trying. My phone started to do the same as you said. I drained the battery until completely dead, there was no charge at all in the battery, then recharged it to 100%. Works fine now. Maybe I just got lucky but won't hurt you to try and will not hurt the phone in any way.