I would be frustrated too.

I don't think that you're overreacting. In my opinion, it's perfectly reasonable to ask your partner to keep a little more space between his friend and himself.

Are you present when they go to dinner or coffee? If not, you could ask to go with. It wouldn't be real appropriate for her to be hanging upon him with you right there! Maybe just being present a couple of times will help her back off a bit.

I wouldn't say that your fiancee is entirely innocent either. It takes two to tango. Messaging one another everyday isn't very normal in simple friendships. Perhaps he's testing his boundaries?? Personally, I would not feel comfortable with that component. That concern is justifiable. While your finacee's words are holding her back, his actions aren't. If he truly is not interested in the woman, he needs to break away a little bit to be more clear to her.

That's my opinion. I hope that everything works out well for you and your finacee!