shooting pain up my arm what is this?

[SMYLEZ]

i cut my ring finger today on the left side (well the lady in the nail salon did it with a file) but it doesn't seem like a deep cut, its very painful when i try to clean it ( with peroxide ) it send this excruciating pain up my arm i feel it in my wrist and up. The pain will then go away when im not bothering it. I'm able to move my fingers with no problem the only time it hurts is when i put pressure on it. and when cleaning Somebody mentioned i may have cut the nerve. I'm just wondering is this possible. or is it infected. there is no puss just pain no redness yet, but paler skin around the bruised area. i just want to make sure its not infected