A lot of good recommendations so far, but i feel like i should reinforce some suggestions.
Shinkai movies (5 centimeters, Voices form a Distant Star, etc.) aren't depressing so much as they give you that feeling of having to cry to move on from what you just experienced while the movie is still going. May not be what you're looking for, but maybe it is.
Now and There, Here and There is outright shocking and unrelenting, and likelier to leave you depressed for a long period of time while you adapt to the fact that the things that make it so disgusting at times are stuff that happen every day irl.
Colorful (WHICH I HIGHLY RECOMMEND) is the likeliest to make you cry because of your own personal stuff, which is the kind of thing that really gets me BUT maybe that's not your thing.
Shindler's List has what is likely to be one of the saddest scenes in cinema ever, so maybe just put that in repeat on youtube until you break.
I remember Koi Kaze being very harsh on my mind way back when, even the upbeat ending left me in an even worse state.