no muscles in your fingers mate, thats what your fore arm is for,
so your straining your tendons or ligaments i guess, i used to get this so i set my levers so they pulled in closer to the bar, feel shit at first but then you get used to it and its alot nice as you have better grip on the lever and the pain stops:)
or just chope it of and forget about it!
edit : also, the tending that tightens your finger to grip the bar runs ont he underside of your fingers, so if you have thin or hard grips you can imagine that the harder you pull your bars the more you squash these tendons, which may also be causing the pain. rest it for a bit, and stretch your hands before and while riding.