I think you are more inclined to try to look at the whole picture than your girlfriend. That is all; don't know how race should have got into this actually. Thing is, from all accounts, it is pretty dangerous to be a Police officer and also black people seem to be more likely to be shot by Police too, so that seems to be why your girlfriend insinuates you may be racist.
I am in Australia and we have heard of all the Police shootings in the US, but we are also aware that there is next to no gun control in your country, very unlike what it is here. You are not permitted to carry, concealed or otherwise, weapons on your person, car etc. without special permits, etc. I even remember a time, in Melbourne many years ago, when even Police officers did not carry guns like they all do now.
I think being a Police officer is going to be a very difficult occupation, and at times you may find your life being put in danger. Quick decisions can mean the difference between staying alive and being shot yourself, if you hesitate. Under those working conditions you will be liable to make fatal mistakes too. I think that this seems to be at the crux of the problem we hear so much about with the Police shooting so many black and white people. There will be no winners in situations where guns are so readily produced by just about anyone, and the Police will continue to make mistakes at times too. The right to bear arms has come at a very high price for the people of the US. Trouble is I don't think there will be any going back to more peaceable times.