I've been in that situation many times before, there's a few things to consider. I can't decide for you whether you should stay or whether you should go, it's entirely your choice. It is healthy to talk to some people, even as an introvert, because you keep up ties with people and if you wanted to ever do something fun with friends, then you would still have friends who would be willing. However, if you don't attend anything, your friends may drift apart and things might get bad, so it's important to attend SOME outings, but not necessarily all of them.
Another thing to consider is, in my experience, when people want to go out and I eventually do go out, I end up having a really good time, even if I didn't want to go at first. A lot of the time I STILL don't go, even if I know i'll have a good time, but most outings I tend to have lots of fun when I go out. So if your experience is anything like mine, if you go out with your friends you'll have lots of fun and you'll build up ties.
I would say go out with your friends either this outing or set up an outing with your friends that works with your time table later.
