I'm going to go on a bit of a tangent here, but please OP, bear with me.
This is a wonderful opportunity for you. Please be excited about this and at the same recognise and address the reality: change is scary. Change causes anxiety in our lives and is difficult to understand and deal with. And thats actually what i think is going on here.
Your life has recently taken a huge turn, yes? You find yourself single and dating again, a situation you didn't think you'd be in and didn't plan for it and now you are caught a bit unawares, yes?
Its ok to be a bit anxious about. And to constantly wonder "is this normal? Am I normal?" because honestly dating is a constantly changing environment and everything needs to be taken and judged on a case by case basis. But just grit your teeth, put on a smile and go forward, because really, isn't that the only direction to go?
So now lets talk about this woman. You seem to think she is keeper, and presumably other then your anxiousness are very happy with her. Well what makes her so great? Is it because she's out going, and vibrant, and moral, and a great conversationalist, and genuinely concerned about stuff, etc? Her social life is probably a big contributing factor to her overall self. She is a whole person and all the positive things you see in her are part of her, and all her relationships and how she spends her free time is part of her.
And now, you are a part of that too. She has a very active social life and yet it sounds like she's really tried to include you in it. You've had enough time together to grow very close in 4 months. That says to me she is making time for you - she is cutting back on seeing her friends. And she's inviting you to join in with her friends - she wants you to be more involved with her life.
And you know what? I bet if you just go with it, open yourself to change, to being more social, to maybe becoming a fan of her sport's team or her musical tastes, you'll be happier and more confident, and maybe make some really good new friends and have some fun. And I bet by being a positive, welcoming, trusting beau, you'll also be building your relationship with new things you and she do one-on-one, things she excludes her friends from.