I have gone through other kind of guilt in the past and have created my own mechanisms to handle it as its one of the toughest to handle. I try to evaluate each action on two factors: How an action affect people(me + anyone affected by it). I treat confession also as an act of confessing.
First objectify yourself by distanting yourself from your emotions.
If confession doesn't bring happiness or alleviate pain for any of the party or consequences are insignificant, then you can choose whatever you want.
If confession affects some party in +ve ways and some party in -ve ways, then we need to rationalize. Confession leads to big guilt mostly when it has strong consequences. A pattern to notice.

. For small consequences we don't even think about it. Jumping red light, overspeeding, saying something when angry, making people uncomfortable or remarks with our approach missions e.t.c.
In your case, your confession will affect you -vely and will affect the girl -vely as well. Both will suffer.
The act of non-confessing, will affect you only(because of your guilt). If you are not able to handle your guilt, then it will start affecting your girl. And if you are sure, your girl won't find out any other way, then its totally your guilt that is in question here.
Be strong and learn to handle guilt. Its one of the emotion and will cause pain to you and people you love in this case.
Guilt comes from what we consider wrong(because of our social conditioning and our experiences). But if you think or feel that you won't be able to handle it, then go ahead and tell the girl. Then its her choice.
Also, if you think that this cheating can be repeated, then its better to tell anyways.
So tell if you think you have potential to cheat again or can't handle guilt.
Forgive yourself and forgive others. Be compassionate towards yourself and be compassionate towards others.