The fingers are controlled by the wrist and forearm, the tips specifically are controlled by the muscle flexor digitorum superficialis and flexor digitorum profundus. These are what give you flexion of your digits, but superficialis is what gives the distal interphalangeal joint flexion that it sounds like you're complaining off. Now, extension is also a big part of this, but that is mainly done by the extensor digitorum and a pulley system of ligaments is used to straighten out the tips. The way the muscles and ligaments themselves attach to the bones of your hand also play a big part as they pass through canals and tunnels which is partly why typists get carpal tunnel.
So, changing your hand and wrist position on a keyboard most certainly may help.
What may help the group to help you, is to determine when it hurts. Is it when your fingers are at maximal extension or during the depression of a key. Do you experience any numbness or tingling before or after? The nerves the muscles are not the same that innervate the hand, and if you're insulting the nerves that innervate the fingers themselves it can be a positional issue as well. However, it may be that you need to find a way to rotation your wrist ever so slightly.
A few people have mentioned that taking ibuprofen is not the answer, and it shouldn't be. Hopefully this thread will stay alive long enough to help you. Otherwise, it might not hurt to see an orthopedist or plastic surgeon that specializes in hand surgery. They have even further training into injuries of the hand and may be able to help you out. I can't promise it, but I suggest it if the pain persists and you find yourself taking NSAIDs (i.e. ibuprofen (motrin/advil), naproxen(aleve)) daily.
Edited for grammar.