You were attacked violently by someone who was aiming for a vital area. (How do you choke someone with your bear hands and you were't trying to either kill them or knock them unconscious?) There's no mention of what circumstances may have led up to this confrontation, so both parties may be partially responsible, but for the specific act of defending yourself, no. You did nothing wrong.
If a man choked you (TWICE) would you hit him?
It should not matter just because it was a girl, sure maybe being the significant other it could be seen as wrong. But your girlfriend choked you first, therefore it is her fault if anything (unless there is some other important part of the story i do not know i.e. a very good reason for choking you).