As a healthcare professional I agree with all of the above advice, get yourself to a hospital and report the incident there. Let them be the judge because at the end of the day you only have one life and one body, don't be too complacent with it!!!
I'm very glad to hear you are ok though, these kind of accidents can be fatal. With a side impact like that, your gf is a very lucky lady (so more reason to get her to the hospital).
Though I will say that as much as the 'right' thing to do is to hit the animal, it can be VERY hard (if not impossible) to shake the natural reflex to swerve since there is only a fraction of a second to react in a lot of cases. Don't feel like you did the wrong thing though, stuff like this happens and there is no right or wrong way to happen, just cause and effect.
That all said, I think you should buy a lotto ticket
edit:
And while I remember, I know I've said to get your gf and yourself to a hospital and I'm not going to be a broken record here; but I will add that with the nature of the accident and what you have described, she could have anything from mild concussion to an ABI (acquired brain injury) so medical attention is a must!!!!
