Is my iPhone5 battery fried or is the screen broken?

I bought my iphone5 in April 2012 and now in January i started to notice a few problems coming up. One morning i woke up to find that my phone didn't charge after i had connected the it to the charger overnight and i do this every night even when its at 90%. Then after i saw this i connected it to another charger and checked i after half an hour and aw that the batter percentage was the same. Now my phone shuts down while im using it and i have to turn the whole thing on again.. Also sometimes my phones screen glitches and changes to a black/green color. I have never dropped it into water but it hass fallen off my bed (2ft high) please help