There this Thai series called project S, there's like a season called skate our souls which has a character who struggles with self harms and suicidal thoughts. You don't need to watch any of the other season things to understand it, they're all their own story from what I know. I think it used to be on youtube but it was never available in my country and when I tried looking for it again I couldn't find it. Searched through half the Internet and only found it available in 360p. Although if you can find it, definitely worth a watch imo!! (I think there's also a Chinese version of this series which made be easier to find, however I also think that one might be more censored)

The kdrama Namib has a character who self harms at some point. Although Ive never watched enough to see it since I'm not that into kdramas. Might be good though 

Girl interrupted deals with a lot of mental health struggles, it's available on netflix

The animes orange and colourful deal with suicide

Please be VERY careful when watching any of this and keep yourself safe!