A companion isn't necessarily a bad idea, but it's not the first thing I would try in your position. You would need to cage them separately during a quarantine period in separate rooms of at least a month, after which you'd want to keep them in separate cages in the same room for a while to get used to each other, and even after all that they might never get along and might need to be caged separately forever. Seems to me like budgies *usually* do well with introductions to new budgies but I don't have very much firsthand experience to back that up, just my impression from what I've seen and heard from others.
Budgies do squabble, that's normal and I wouldn't call it violence or worry about it unless it's causing injury.
I would say you should absolutely focus on making your current situation work before considering bringing a friend into the flock. Your budgie's cage needs LOTS of destructible toys, and it's good to swap them out and rearrange regularly so there's always something to explore. Radio/Music/Podcasts/Youtube videos/aviary sounds are all things that you can leave playing in your room while you're at school so that your budgie feels like he has some company. When you are home, please make sure to spend plenty of time with him, ideally an hour of out of cage time a day.
If you try ALL of that and he still seems lonely, AND you're prepared for the possibility that you may need to find space for a second cage for the long term, I would consider a buddy.
Edit: sidenote, is your house completely empty during the day? Do either of your parents stay home or work from home? Another solution would be to relocate the cage to a place in the house where your bird would have company, and you can always bring him back to your room to hang out with you once you get home, depending on the size of the cage.
