is it okay to say this to my friend?

It is more than normal to feel what you're feeling; we all have. You're just jealous that you're introducing people, and they're becoming friends with each other, because you feel left out (because they were "your" friends). You don't want them hanging out alone without you, because it makes you feel excluded and bad. It's always always awkward when this happens to anyone.

It would be best if you can look at the benefits of her being able to get along with your other friends, because you can have a fun group all together. If you want her to just stop, you have to tell her that you think it's great she's so social and wants to get along with people, but you just don't like how she reaches out to all the people that you introduce her to. I wouldn't make her unfriend this person, just tell her for in the future to tone it down and just play the role as a "mutual friend" instead of a "good friend" to people you introduce her too. If she is a good friend, she might be confused, but she should listen to you. It's ok to say "i really know how dumb this is or might sound, but it bugs me and makes me kind of jealous and uncomfortable when you always try to start friendships with people i introduce you to. i like having people i feel like are "my friends," you know?"

Honey, if she was your true bestfriend you'd both be equally friends with each others friends if that makes sense? I mean your bestfriend should also be friends with your friends and you should be friends with her friends because you guys are bestfriends.

I mean its complicated to explain, but I don't she think she'll say she minds 'unfriending' your friend on facebook but im sure inside she will, and I think that you're scared you might lose her because she might be getting too close with your other friends but if you aren't sure, tell her how you feel first - dont just tell her straight away to unfriend your other friends and then you guys will sort this thing out :)