To give some background information, I a'm not only majoring in English, but also in physics.

"I am" is correct (and may be more correct for an English exam), but "I'm" sounds more natural, and is more common amongst native English speakers.
Though the second "in" is correct, it sounds more natural to omit it.

When I joined the class, one guy was nice enough to sit next to me, and we started to be friend each others.

Your sentence wasn't incorrect at all, it just sounded a little off.

We are friends during school, but outside of school we hadve basically no contact.

Be sure to maintain the same tense through out the sentence. "are" is present-tense, "had" is past-tense

This changed recently changed.

Your sentence was correct, it just sounds more natural with the other word ordering.

I feel like he hints at wanting to be more than friends, and I am just trying my best to nicekindly tell him off.

"nicely" works, but "kindly" sounds slightly more natural. "just" is an unnecessary suggestion, but it makes the sentence sounds a little bit more like a native English Speaker (In terms of casual speech).

A few months ago he started following me on Instagram and he added me on snapchat, which is totally fine by itself.

However, he developed the habit of constantly writexting me, and especially when he is drunk, which his concerningly often, telling me how much I mean to him, that I am nice and pretty, and that he "wants to take our friendship to the next level".

"writing" gets your point across, but it sounds a little bit weird. Other more common words could be "chatting", "messaging", or "snapping" (like you used below), and probably others?

Additionally, he i's constantly snapping me, constantly updating me about his life.

"he's" is more casual than "he is." Most native speakers tend to use contractions of <INSERT WORD HERE> and "is," rather than both words separately in casual speech.

This is something I do non't really mind.

"don't" is more casual than "do not," and is far more frequently used in casual speech (sometimes even formal speech).

However, he also started updating me about every single girl he i's talking to.

casual speech.

Every half an hour or so, I get a snap saying "I just talked to *name of a random girl*".

Since this is a quote, it could actually just be the case that this is how this person is writing, but the past-tense makes more sense here.

I really could non't care less.

casual speech.

Why would I want to know what girls you a're talking to?

casual speech.

I feel like he is trying to make me jealous, but I just really just do not care.

This word ordering sounds just a tiny bit "better," and is also (somehow) an instance where it sounds "better" to not contract "do" and "not" into "don't." Additionally, you could also go with the following suggestion.
"I feel like he is trying to make me jealous, but I just really don't care." (back to the contraction of "do" and "not" into "don't" sounding "better")

I do non't know how to tell him that I do non't want anything from him, but I also do non't want to lose my friend.

casual speech.

This really annoyed mye, because why can't he just be friends with girls, and why does he have to ruin everything?

"why can't he just be friends with girls" and "why does he have to ruin everything," are both separate thoughts, and should therefore, be separated by a comma.

To start this little post off, I would like to say that this is probably something I should post on Reddit or something.

However, I kinda need to learn and practice my English for school, since I have my final exam soon.

as long as you don‘t write ‘kinda’ in your exam :P

My physics class is full of guys and I am tohe only girl there.

I am his type, and he has a long history of ruining his female friendships because he always develops a massive crush on them.

Worked without “always”, but I feel like it made the rest sound more natural.

This is incredibly annoying for me, because I just want to pass physics and want to have some friends there.

redundant

A few months ago he started following me on Instagram and he added me on snapchat, which is totally fine by itself.

typo

Additionally, he is constantly snapping me, constantly and updating me about his life.

if you wanted to keep both ‘constantly’s just to show how annoyed you are i would replace the second comma with a hyphen

Every half an hour or so, I get a snap saying, "I just talked to *name of a random girl*".

And in the politest way possible.…

This really annoyed my, because —why can't he just be friends with girls and? why does he have to ruin everything?

To start this little post off, I would like to say that this is probably something I should post on Reddit or something.

My physics class is full of guys and I am tohe only girl there.

They all knew each other before I joined the class.

We are friends during school, but outside of school we hadve basically no contact.

A few months ago he started following me on Instagram and he added me on snapchat, which is totally fine by itself.

However, he developed the habit of constantly writing to me, and especially when he is drunk, which hiappens happens concerningly often, telling me how much I mean to him, that I am nice and pretty, and that he "wants to take our friendship to the next level".

Every half an hour or so, I get a snap saying "I just talked to *name of a random girl*".

This really annoyed mye, because why can't he just be friends with girls and why does he have to ruin everything?