K.F.
Your daughter sounds like me when I was her age and beyond. There is good news. She may just be an introvert. What has really helped me over the years was acting and dancing. I also used to suffer from sever stage freight but worked through that too.
Have her join an acting class or find some other kind of thing she can do and get good at that interests her. Having tons of friends is not necessarily essential to becoming a healthy and whole individual. The more she gets to know herself the more confident she will become.
I used to have parties where no one would come either. Please stop throwing her parties like this. She may be better served with a smaller more intimate group of 1 - 3 girls but it is helpful to have things in common. Perhaps she could take classes in martial arts, art, drama, music, dance, fencing, or something else like this where she could establish friendships. Even learning chess and competing may help too.
I've always been the odd duck but now I'm a beautiful swan. Just understand some of our beautiful children take longer to blossom and my great grandmother always said the later you blossom the later you wilt. She really loved me for me and that really helped me be fine with being different.