Linda, I know what you mean. Having the right group to hang with is critical. People should feel uplifted by those around them, not depressed, lonely and rejected. And often its family members who make you feel this way. I took a huge step and moved to a remote city to start over. Not everyone has that luxury, but I have few possessions, so for me it was easy. I like my new town and I'm meeting nice people.

The approach that has already been mentioned here also works for me. I ask them "what brings you here tonight?" Then the next question explores that: ie questions about their work or their partner or grandson or whatever it is brings them here.
If you get stuck, look around the room and say to anyone, "wow, a lot (not many) people here tonight hey?" I wonder who these people are as I don't know anyone it seems.
Just keep the focus on them or the organisation - as long as it is positive it will keep flowing. If you say something negative odds are they will clam up - or want to tell you secrets - you don't want that.

When I am in a group and I don't know anybody, I feel the crowd out. I will go get a drink first, and just watch what's going on. When I am introduced, I will be polite and listen. Then I usually pair off with one person and start getting to know them. If we click, I will hang out with them for awhile and enjoy the company.
I never talk about my anxiety, depression, or other problems when socializing. I save that for a therapist or support group.
Here's what I will talk about: if it's a woman, I will ask her about her man, blah blah, how long they've been together. If the place is new to both of us, I will explore it together whether its finding a ladies room, or my assigned seat. If the focus is on a band, I will talk about the show. If its a baseball game, I will tell her I think watching the baseball players work out is my favorite part of the game. Same with football. I focus on what's going on around me and comment on it.
Finally, I don't cling to people, I work the crowd and if I am uncomfortable or tired, I just go thru the motions and I don't stay too long.

One of the tricks is simply to ask others questions about them - if you can get someone talking then they will think you are an amazing conversationalist even if you simply prompt & listen. Old saying..."The more interested you are, the more interesting you become......" xx😎

Are these "girls" your close friends? If they are, then I would just tell them about my social anxiety. It might make the situation easier for you. If not, then just put on a happy face and enjoy the evening. You know what they say, "Fake it until you make it."