I’m sorry you’re feeling this way, but know that you are not alone. Did you read this? Please do: http://talk.collegeconfidential.com/college-life/2016222-to-those-who-feel-lonely-homesick-friendless-think-they-chose-the-wrong-school-etc.html#latest
I think there is plenty you can do to make your situation better. What should you do? Be proactive. You can ask people to lunch. You can send a snap. You can get involved with a club, or volunteering, or the campus ministry where you can meet like-minded people. You can get a job in a busy place on campus like the bookstore. You can go to the counseling center. You do not have to be alone, even though you feel lonely. Eventually you are going to find good friends.
I don’t see that you said you’ve had depression before. Regardless, go to your counseling center at school ASAP. They are talking to MANY kids who feel like you.
To answer the question, I do think you are misinterpreting some of what is going on with that group. I think you are seeing everything as a slight against yourself and a deliberate exclusion of yourself. I doubt that anyone’s actions are that deliberate, especially towards you. I suspect that you’ve found yourself in a similar position to the nearly 17,000 other people who have read the post I linked above, and you’re taking things too personally. When you’re feeling alone and awkward and lonely and uncertain about the new place you’ve just moved to, yes, it’s easy to believe the worst.
Please have some perspective. There is nothing wrong with you that isn’t wrong with tens of thousands of other kids who are freshmen in college. All those kids who you THINK have solid friendships, well, some do, most probably don’t. You need to give it time because good friendships don’t happen in just a few months. You haven’t been left out as much as you just haven’t found all of your people yet. None of these early friendships are set in stone. You can always keep making friends.
You aren’t looking at the positives: you do have some friends. You like your roommate. You’ve been invited to do things. You are proactive enough to do things on your own.
Let’s look at what really doesn’t matter: you weren’t invited to something. This happens. You have to brush it off and move on. It will happen again, I’m sorry to say. You can’t be invited to everything and it doesn’t mean people don’t like you. None of them reached out for lunch. Did you? Secrets are just that. Secret. It doesn’t matter if you’re privy to them.
I strongly advise against a single dorm. Very isolating. I also advise against transferring. What’s going to be different at a different school? Has anything changed about YOU that will make it easy to transfer? Transferring has its own challenges and is really best done when a student absolutely does not fit in or wants to study a subject not at their current school.
Be proactive. Hugs to you.