So, first a point about threesomes, foursomes or similar. There's nothing wrong in principle with doing them. Sexual experimentation is not only fine but often it's positively healthy. You've said that you didn't realise that your girlfriend was "like that", which begs the question, like what? Somebody with a high sex drive? Someone who wants to broaden their sexual horizons? Someone who enjoys sex and wants to have different experiences of it? There's nothing wrong with any of this providing it's consensual and done safely.
However, that said that there are two highly relevant points to this particular situation. First, there's no obligation on you at all to want to be involved in threesomes or foursomes. If you are not comfortable with it, then don't do it, whether that's as part of a relationship or on your own account. Lots of people close off their minds to this sort of thing when they'd probably enjoy it in the right situation and with the right people, but that's really neither here nor there. If you don't want to do it, don't do it.
Second, whilst that's a good enough reason to not go ahead with this in and of itself, engaging in sexual activity with others as a couple is something you need to be very careful with. It's not something to immediately rule out. Far from it, plenty of couples do to it and enjoy it, but it is something that requires very clear communication before, during and after. It's also something that requires a high degree of maturity to get right, and one that with the best will in the world, most people don't have in their 20s. It is absolutely never something that should be done when the relationship is in difficulty, or as a way to solve problems in a relationship. It can only end badly in that situation, and that is the situation you have here.
So from very angle, it's a bad idea here and one that you shouldn't be pressured into anyway because it's not something you're interested in. I would also be concerned about the fact that your girlfriend suggested this shortly after suggesting that she deserves better than you. That strongly suggests to me that she is certainly not mature enough to engage in this sort of activity as part of a relationship. It's something that you have to experience and work through together, and absolutely not something that one person should be using almost has retribution over the other.
So in short, no, do not do it when you don't want to, and don't do it unless you have a significantly stronger and mature relationship than the one that you have here. You need to be focusing on repairing the issues within this relationship. And that most definitely does not include a threesome.