my phone will randomly start being incredibly slow

I got my phone about a week before christmas of 2013 and for awhile it was good & then it randomly started to become incredibly slow & sometimes just shut off. Now it wasn't freezing, so don't confuse the two. It's just anything I do on the phone it takes forever to do as if it's sticking. It takes me several & several swipes to even change screens. & then it will randomly stop. But when it is being very slow, it takes 4x the normal time to charge. I'll go to bed with 10% charge & wake up about 8 hours later with just barely 50%. Do I need to buy a completely new phone or is there something I can do to fix this easily??