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Okay, first of all, there may be a cause/effect and there may not, but in either case, you want to be very careful if you talk about this with her, because you don't want to cause her to associate something enjoys with something that traumatized her.

So as for how to go about it, a few resources and a few suggestions. First, the resources:

If you want some good reading material about this, check out Screw the Roses and SM 101. These two books are among the most respected when it comes to this topic matter. You might also want to get yourself on Fetlife, a community you can use to look up more advice, perhaps even in specific areas.

Now, as for my own advice:

You two should start with something called Negotiation. This is a process where you decide what you'll be doing before you do anything. I know it seems sexy to be surprised, but you can cover a lot of ground so she won't necessarily be able to predict what you'll do, but know that whatever you do will be something you agree on.

Take some time to get a feel for different things you could do, and then find out from her what she's interested in, what she does not want to do, and what she isn't sure about. Maybe her idea of "violent" isn't the same as yours. You need to get a very clear idea of what she wants before you do anything.

One thing that it seems like just about every girl I've encountered seems to like is having their hair pulled, but it has to be done in a specific way - don't just grab a fistful and tug. Instead, put your hand flat against the back of her neck with your fingers pointed up and move your fingers up the neck and into the hair as close to the scalp as you can. When you're at the base of the scalp, grab a handful that's as close to the scalp as possible. Doing this feels better, isn't quite as painful, and gives you some good control over where to move the head. This way you can be more forceful without causing not-fun pain.

For any kind of new play, always start slow and as light as possible. You need to ease into it, both because she's still deciding what she does or doesn't like, and because even if someone likes something that doesn't mean they want to go from zero to sixty right off the bat.

Play using floggers, paddles, canes, or bare hands used to strike is referred to as "impact", and different people have different reactions to it depending on the location it is used on the body. Usually, the butt is a pretty safe bet for most kinds of impact, but there's also the boobs and inner thighs, and the genitals. Again, start light and gradually increase it to see what kind of response you get.

There's also light biting that you can do (again, gradually work your way up), and you can do nipple torture, tugging on them or flicking them - some girls like this, but some absolutely hate it, so be careful.

For face-slapping, you want to be careful with both your aim and how strong you hit. Again, start soft, and you need to be sure to get the cheek/side of the head. Be careful not to get the eyes, mouth, or jaw.

Finally, while you may be tempted to do some choking/breath play, be aware that this can be extremely dangerous, and you should read up on the risks associated with this before even considering it. I won't tell people outright not to do it, but be warned that it is not to be taken lightly.

Hopefully this is a good start for you. Good luck!