First step would be to breathe. While it always seems like everyone else is having more fun than you and doesn’t have a care in the world, your feelings are actually incredibly common. I think social media has been a factor, because you always see what looks like everyone else having a grand old time and think you’re a boring loser, but the reality is everything on social media is wildly exaggerated.
Even as a freshman with decent social skills, it took me an entire semester to start to find friends I really gelled with. I am going to join the party and HIGHLY recommend clubs as a way to meet friends. Easiest thing in the world because a.) you already have common interests with everyone and b.) you don’t have to stress about making plans/not being invited; it probably meets regularly at a publicized time. Try a few out and see which ones stick. There are major-based clubs, interest based (I’d bet you have a video game club or something similar), school-based (work to plan campus events, student government, admissions, etc.)… I bet you’d find at least one or two you really enjoy.
Reach out in your classes to see if people want to study after class, or pick a group project partner who seems cool. Though I’ve actually never made any very close friends in my classes, the vast majority of my friends have.
As far as your roommate who you “thought” was your friend… They probably are. I have a handful of best friends in the entire world and am not always included in the plans. Often, there are good reasons for doing so-- perhaps they don’t know the host of the party and wouldn’t feel comfortable asking to bring a guest as a guest. Maybe they know it will involve people or activities I don’t like. Maybe the plans just happened so spontaneously they didn’t have time to invite others. Sometimes, you just want to hangout with a different group for a little. Other times, you might genuinely forget. If possible, don’t be afraid to press. “You know of anything going on tonight?” or “You mind if I tag along?”. Don’t stress if they say no, but ask a few times over the course of time. If they do take you somewhere or seem bothered at all, feel free to say to them “I really don’t mean to be a pain, and I’m sorry if I’ve seemed clingy-- I just don’t know that many people yet and you and your friends are always a good time. Let me know if you ever need a break from me or anything, but I really appreciate you letting me hang.” For what it’s worth, I made one of my best friends in the world this way. He didn’t really have a “group”, but we liked hanging out so he would sometimes push to ask if he could come with me and my other friends, to our parties, whatever-- and now we’re all good friends. So it’s not a crazy ideal.