I can turn my phone off but the it starts right back up. How do I fix this?

This can happen if the iPhone Charging Port pins are shorting. Clean the iPhone Charging Port with a clean dry toothbrush. If you have water damage and have already voided warranty and the clean dry toothbrush does not fix the problem, then try cleaning the Charging Port with the toothbrush and a bit of Isopropyll Alcohol.

Otherwise with Warranty, which you should still have, take iPhone in for Warranty coverage of this problem.