I moved away from home when I was 19, and felt the same way as you do. Later when I moved to Sweden and started working there after several years of working my ass off trying to get a decent job, taking all sorts of part time jobs to get by, and finally ending a 7 year relationship (with kids), I was quite depressed as well.
I moved away from home because I couldn't stand living under the same roof as my adoptive father. THe entire situation topped it self when he pulled his shotgun on me for reading comic books two days before Christmas, in stead of doing homework. He refused to listen to me try and explain that I was actually reading them for a school project. A minimum 60 page analisys of a subject that was to be delivered in the spring. I ended up changing my subject to my favorite author at the time to satisfy him, but got in turn too little time to do a decent job on it, and got a poorer grade than expected.
Back to the shotgun insident. When he had shoved the barrel up my nose I told him with a calm voice to shoot. He'd be the one that would have to live with it the rest of his life. I didn't care.
He packed away the gun and the day after he took my sister with him and left for a 10 day vocation in Spain. I didn't talk with him again until after I had moved out that following spring, and that was first after he and my mom got divorsed some years later, and he had re married. We only spoke that one time, and never since. He's hiding out in Spain, Today I think he's hiding out in Spain after an incest case where he had abused his daughter (My step sister). I witnessed against him in the trial. I wasn't actually in the court room, but was interviewed by a police officer where I live. Allthough he never abused me in any way, he did treat me like I was his personal slave. Since I was 5 years old and until I moved out he was constantly giving me jobs to do that most grown ups would not have managed. For example when I was 7 he tried to force me to dig a ditch that was 20 yards long, three feet deep, and three feet wide. He wanted the job done in three days.
So you understand that moving out was a huge impact on my life. First off I had about 400 Dollars of income a month to get by on, and the room I rented cost about 300 $ a month. That was in 1989, and 100$ a month to cover schoolbooks, food and clothes was way under the poverty limit even in those days.
I fell imediately into a depression like yours, and only maintained my job, and spent the rest of my time either sleeping or out fishing so I had some food on the table. I slowly got over the depression and told my self that I had to change my life or I'd end up in ruin. I had some really tough years trying to get ends to meet, and I still do, but now I have a home of my own, a great girlfriend. Together we have a beautiful little daughter, and my two boys from my previous relationship come to stay every summer. They ahve both grown into some really great teenagers.
So my advice to you is to is to lie low during any depression period, but keep up your work, and rather catch up on the rest when you feel like it. You may use a couple years or two extra with your studies. That's OK as long as you reach your goal.