Minecraft is designed to be played on a 16:9 aspect ratio monitor. Looks like you still have a 4:3 . When you go full screen it trims the sides of the viewable area to fill the screen to the top and bottom. So, I'd suggest you to play in windowed mode.
This can potentially happen if you use a monitor that has the Aspect ratio of 4:3 or 1:1 The game is designed for a norma 16:9 aspect ratio monitor, so some things get cut out and glitch, like in your screen shot your sword is out of the screen [ the one you are holding ] I think switching to a 16:9 Ration monitor, will fix this.
if problem cant be resolved by switching resolution, backup your .minecraft folder and do a fresh install mc to have a fresh rp-file