Vocals are mixed nicely and I like the simplicity of the beat, but the vocals being off tune make the song uncomfortable to listen to.
There are two ways you could theoretically go with this: a second take more on-tune, like you had posited; or alternatively, leaning into the off-tune nature with some vocal processing. How exactly you would do this is definitely a fun and challenging little puzzle, but I can't think of any ideas off the top of my head that would help sell the off-tune aspect as symbolic of vulnerability or emotional damage. But hey, Alt-Rock does that all the time, so it's not completely impossible.
Honestly though, props for putting this out. It can be really scary to sing about vulnerable stuff like this and to work with your voice when it's minimally-processed. While I think the end result leaves something to be desired, I think this is a good way to get your feet wet when it comes to stuff that's a little more heavy.