advice for someone who is very homesick

I am 20F American currently doing my fall semester abroad in Seoul, South Korea. I have been here for about 5 weeks with 12 more weeks to go and am feeling super homesick. Last week I started to really miss my life back in the US. Things here are extremely different from what I'm used to as far as different food, societal norms, and the beds are quite hard so I sleep poorly. My boyfriend of over two years is also back home and my family. I don't talk to my family that much because of the 13 hour time zone difference. I live in a dorm on campus here and share a very small room with a roommate, we don't get along well and had a big argument last night which exacerbated my homesickness. I am also a huge introvert and love being by myself but with a roommate I don't get a lot of time to myself in the dorm.

I've spent the last couple days feeling too sad to go out and explore Seoul and really wishing the time would fly by so I could just go home.

Please give me advice on how to deal with my homesickness and also what kinds of things to do to prevent me from spending too much time in my dorm sulking. Thanks all!

LMK if this is not the kind of post for this subreddit, I'm new to reddit and how it all works.