If you don't know anyone using a sling in prone, why would you even respond to this topic?
OP, is it possible you are not pulling the trigger straight back? If not, pulling to the right would suggest that you have too much finger on the trigger, or the trigger shoe is too far rearward for your hand. Adjust your trigger hand position while dry firing until you are pulling it straight rearward every time and make a mental note of where on your trigger finger the trigger needs to be. Some people will tell you that the trigger needs to be on the pad, of your finger tip, others will say the distil joint - they are all wrong. The only correct spot is the one that results in straight rearward trigger pull, wherever that might be.
Plenty of other possibilities here, but that's my first guess.
Easiest way to quickly adjust elevation when shooting with a sling is to slide your body forward and back very slightly while keeping your arms planted. Forward will lower POA and rearward will raise it. Remember that anything you move will have an effect on your NPA, right down to your toes. The more you shoot this way, making these small adjustments will become second nature. For more major adjustments, variations in sling length, handstop position(if you are using one), length of pull, and height of buttplate in the shoulder will all change NPA quick.
Good luck.