I don't like to bring bad news to this forum but I doubt the DA will let this one drop. Usually they evaluate these things on the seriousness of the injury and based upon what you said it sounds like there was substantial injury to your girlfriend. Staring the courses on your own is a good idea and may score some points with the DA but if I were you I'd forget about any profession in which I am required to carry a gun. Your gun rights are gone for life.
With a misdemeanor conviction for domestic violence on your record, you would be prohibited from possessing a firearm for 10 years from the date of conviction. There is a one-time exemption for people that are employed as peace officers [but there are hoops for them to jump through - see Penal Code section 12021(c)(2)].