My phone keeps shutting on and off and wont charge when plugged in

Cell phone batteries have what is called a "memory" over time if they are charged without being fully drained they can start to not hold a charge. Unfortunetly the only fix for an issue like yours is to purchase a new battery. Your local retailer / service provider should have batteries in stock or they can order one for you.
It is recommended to allow the batteries to drain completely before charging, then allow at least 8 hours or more to fully charge. Most cell phone will show a full charge after a few hours, but this is more a fault with the software that check the batteries charge, then an actual indication of the battery being fully charged.