Oh I really feel for your DD, and you.
My DD has been at her new 6th form just over a week now. First day was all exciting and new, then a couple more days on she said similar things to your DD about trying to connect with people. Because she is going to an existing (much bigger co ed) school there are very established friend groups, but with more than 100 external students, still plenty of new people to bond with. She had a couple of bad days when I got texts at work saying she wanted to leave and come home because no one was talking to her.
It turned out they were all sent to a large hall for free periods, and when she had a free without anyone familiar (she does know people, just not her closest friends) no one welcomed her to sit with them, so she felt alone. We talked through the tears, she has changed one of her subjects and has a group of people who are budding friends. I could only advise her to take it slowly, not to try and find a best friend immediately and do as much homework as she can in her free periods if there is no one familiar around her.
Two days on she is much better. She is hanging around with a new group of boys and girls from another external school who sound lovely and kind. She is also focusing a lot on her subjects and has now signed up to enrichment things like mentoring younger students so is very positive about doing that.
I just want her to try and be ok if she is on her own for any reason and have the confidence to ignore unkind people and do her own thing. Easier said than done when you are 16 though. Getting used to moving from an environment where everyone knows her and respects her to one where is is one of hundreds of students, and no one knows her has been a shock, but an experience I believe will help her in the future, especially if she goes to uni in 2 years.
I hope your DD has better days soon, can she sign up for anything enrichment wise which might distract her?