Hello there and welcome. I had a similar experience to yours (though not as extreme) when I watched Neon Genesis Evangelion (I really don't recommend this show if you're having a tough time with your mental health. It is possibly the most traumatic thing I have or will ever watch and it's not something to watch in the wrong state of mind). It was actually the show that got me into the anime and it sent me into a serious existential crisis and depression for about a month. I almost failed my work experience module at university because of it and it seriously changed my outlook on life. Mine was more a sudden realisation of nihilism - which wasn't nice, and would've been quite disturbing if I didn't find these sorts of things fascinating. Nevertheless, I did eventually get through it.
It sounds to me like your depression is connected to an immediate loneliness, mainly from the fact you say that getting attached to characters and wanting an "anime relationship" are primary contributing factors. Believe me, I understand this all too well. It was something I experienced a lot when I was your age (I'm nearly 22 now) as a below-average looking, socially anxious teenager. I remember always wanting to have a relationship similar to characters from my favorite shows, anime or otherwise. It caused me to take actions in pursuit of that goal which were totally unrealistic. This is stating the obvious somewhat, bjt imagine if Tsundere's, for example, really existed - it would go very differently to how it does in anime. I'd like to say that it's easy to break out of, but it isn't. All I can say is what helps/helped me - focusing on that which I had in the present, not placing too much importance on the perceived NEED of a relationship (especially one similar to that shown in anime), but also a general acceptance of myself for who I am.
Hope this may help you a little bit. If you want to discuss further please send me a PM. My name is Michael