I'm not seeing a compelling case for self defense here. She pushed you. Presumably you could have just backed away at that point to avoid further contact with her. Instead, you escalated the conflict by punching her in the head, a more forceful and damaging attack than what she did to you. In California, you have a good self-defense claim if all of the following are met:
- It was reasonable for you to believe that you were in imminent danger of suffering bodily injury;
- It was reasonable for you to believe that the immediate use of force was necessary to defend against that danger; AND
- You used no more force than was reasonably necessary to defend against that danger.
I have a hard time seeing a punch to the head as being “no more force than was reasonably necessary” to defend yourself from a simple shove, especially if you could have walked away from her so that you weren’t in danger any more. But then, I wasn’t there to see the exchange that took place.
You really need to get an attorney to defend you on this battery charge. Maybe something you haven’t mentioned here would give you a good defense. A conviction on that can cause you a lot of trouble. You’ve already said it would cost you your job. It may also make it hard to find a new job if you get fired. And there is the possibility of fines, jail time, etc.
The woman you hit might also sue you for damages from the injury she suffered from your punch.

