I did a bad thing, and now I don't know how to fix it

I'll try to make this as short as possible. My fiancee and I have been together for 4 years. We got engaged over two years ago, but we have both been under a lot of financial stress so we put off the wedding. To add to our stress, my fiancee's mother has fallen seriously ill with cancer. For the last year or so, we have been fighting a lot. My fiancee is naturally a loud person. When I say "loud" I don't mean she screams or throws fits. She just naturally projects her voice, and it can get shrill and carry a lot, especially if she's angry or upset. Because of her loudness, our neighbors have always heard our fights and it has been a huge source of embarrassment for me since I'm naturally a quiet person. I was friends with out last landlord, which was a good thing because we got a few noise complaints for our fighting and probably would have gotten kicked out if I wasn't friends with him. Last week, we were at my mother's house with other family members present in the next room when my fiancee and I started fighting again. I admit that I picked the fight over something really petty. My fiancee was getting ready to take her mom to chemo and get test results the next day so she was already on edge and she exploded right back on me. She was talking really loudly, not screaming or anything, but loud enough where my family could probably hear. I told her to be quiet twice but she just kept telling me to give her space, which I didn't, because I feel like she needs to learn how to fight without projecting her voice so loudly. I told her to be quiet for a third time, then I mentioned she was embarrassing me and making herself look crazy. She said, "I don't care. If i'm such an embarrassment, don't pick fights with me!" That made me lose it. How could she not care that she was humiliating me in front of my family?? Before I could even rationally think about it, I slapped her across the face. It wasn't hard enough to leave a bruise or anything, but there was a red mark that faded after a few minutes. Instead of being quiet, she looked stunned for a second and then started crying hysterically like she was in shock. I then lost it again, and grabbed her by the throat and covered her mouth with my hand, trying to get her to be quiet so my family didn't hear. In the process, she fell backwards and smacked her head on a wooden desk in the room. Now she is saying that she wants to end our relationship. She keeps saying I "attacked" and "beat" her and I'm an "abuser." While I definitely agree hitting her was wrong, I think she is over reacting a bit. I showed her pictures of women who had really been "beaten" like Rihanna. My fiancee has a small bump on her head and that's it. It's not like she is covered in bruises and cuts. She also refuses to acknowledge her part in it. She just keeps saying it's completely my fault. She says it doesn't matter if she was loud, that there is never a reason to hit her. While I agree I didn't have a "reason" to hit her, I don't like how she is acting like an innocent victim who was just hit out of no where for no reason. I know that I will never hit her again because I feel really bad. I've never hit a woman before. How can I make her see that this one incident isn't worth throwing away our entire relationship and our future? How can I fix this??

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