I assume you’ve already seen this page on W&M’s website? Transfer Students | William & Mary
Looks like they do have some transfer info sessions coming up that might be a good way to explore the idea more: W&M Transfer Information Sessions | William & Mary
Also, I don’t know how close in distance you are to W&M or if you were accepted there before or have a reasonable chance to be accepted as a transfer. I have no idea how many transfers from other colleges they take although I know they have a program with VA Community Colleges and Richard Bland Junior College, but if you are an academic superstar at your current school and are sitting on a previous acceptance to W&M and feel fairly confident that you could get in there and you are close in physical distance it might be worth it to go over there to some public events that you are interested in like a sports ball game or a theater event or something of that nature that the general public is invited to and see if you can get a better feel for whether you would fit in. Maybe strike up a conversation with W&M students and see if they seem friendly.
You can always apply to transfer to W&M and some other schools and still work on your social situation at your current school. You are not obligated to accept a transfer offer so if you find yourself settling in a little better later this semester and in spring you can say no thanks to a transfer acceptance, but it would give you some options to put some transfer applications out there.
My gut feeling from what you have told us is that you may be able to fix the social situation at your current school and save yourself the headache of transferring. Not all of my daughter’s credits transferred but she had some AP credits that made up the difference.
As a parent I felt swayed by the fact that her new school is better academically for her major and has pretty robust study abroad and internship programs. It does cost more so that was not ideal, but she did still get a scholarship. If she had wanted to transfer to W&M and it didn’t cost too much for us (we are not in VA) I would definitely have been okay with her trying that since it is an excellent school.
If the finances and academics work out at W&M for you and your family it is an excellent school and they do take quite a few transfer students, but you will still have to work at making friends there, too. All your credits may not transfer and it might take longer to graduate. All things to think about.
In any case you don’t need to be friendless and miserable for your time at college, but you may have to really work at making friends. Invite people over to your apartment or invite them out to get coffee or to study or to a campus event whether you are at W&M or your current school.
Also check out the r/williamandmary subreddit Reddit - Dive into anything and maybe ask your question there, too.