Stop cutting your toenails short. To relieve the pain you should soak your feet in warm water.
Cutting nails short is okay, so long as you ensure that you cut them straight across. Don't let them get cut in a curve as when this grows, it greatly promotes the growth of in-grown toenails.
Also, I suggest that you follow the above advice with warm water, but add in some salt as well. It may sting a bit, but it'll do the wound good. Make sure you wash it regularly and I suggest bathing it and drying it nicely every day until it goes.
I used to have a very similar problem (And occasionally get the same problem) as I have a nasty (as far as my family is concerned) habit of biting/picking my finger/toenails. Since I bite them, they are short and rounded, which can lead to problems if they grow. I also tend to go too far and sometimes end up damaging the skin around the nail or take off sections of the nail. I've exposed the nailbed under my thumbs before and many multiple times on my little toe.
In fact, I've got half a nail missing from my little toe on my right foot right now. I'm determined to remove the rest even though I know for a fact that it will bleed and will be sore when I walk for the next day. :c
So, take better care of your feet. Wash them and make sure you cut them regularly to avoid you getting ugly long nails, which can trap dirt, but make sure they're not too short and are cut straight across to avoid damage to the nail or ingrown toenails.