You should definitely NOT be playing with your fingernails on the strings :confused: I can't even picture what it is that you are doing. Either way, I can tell you it's wrong if you are damaging your fingernails. Always be playing on the tips of your fingers. Like if you are pointing at the fretboard through the string. Neither your nail, or the "pads" of your fingers should be touching the fretboard. Sometimes the pad is ok, but NEVER the nail......you aren't by any chance playing with your hand backwards and upside down are you :p .....that's the only way I can picture you playing with your fingernails holding down the string.

"A minor" is one of the easiest chords for me, and I have short fingers also.
It's just 3 fingers and they aren't even placed in an odd way. If anything, this is one of those most natural feeling chords for your hand I think. First let's see if you are actually playing it "correctly":

First finger should be on C (2nd string, 1st fret).
THIRD finger should be A (next string up on the 2nd fret).
Second finger (middle finger) right above the 3rd on E (4th string, 2nd fret).

For ANY chord that gives you trouble, there is always one piece of advice that everyone will always give you:

Start by placing one finger at a time. I would start with the "top" or middle finger. Place that down on the second fret and make sure it rings clearly. Then just add the next finger (3rd finger on A) and make sure they both sound clearly. Lastly, simply add the first finger.

Found this picture online:
http://i.ehow.co.uk/images/a04/or/pq/play-aminor-chord-guitar-800X800.jpg