Shallow scars from cutting yourself sometimes go away within 3 to 4 weeks but if the cut to your skin was deeper than usually the scars will be with you forever and never go away.
I've used makeup concealer before to cover up cut scars that wouldn't go away and although you can sometimes still see a bit of the scar it does cover up most of the scar where it's not really that noticeable.
The deeper the cut the more severe the scar and the less likely the scar will go away.