Dear fellow seeker of a feeling,
I had to sit on your question for a few days, for something was in the back of my mind which I couldn't remember anymore. Just now it hit me: what you are inquiring about feels very much like one of the underlying themes of Haruki Murakamis "Colorless Tsukuru Tazaki and His Years of Pilgrimage" (2013). (1)
Wishing to not to spoil the novel too much for those who wish to experience it themselves, I will keep plot points to a minimum. Mr. Tazaki, the protagonist, finds himself cut off and pushed away from his circle of friends without warning or being given a reason. Suddenly, he is isolated, and the experience crushes him. The story then continues with his long years afterwards trying to rebuild himself and refitting into society, finally learning the true reasons behind the ostracism.
Why do I remeber this novel specifically? I must admit, it is not directly an answer to your question, since it does not contain the feeling of haven't being built for society. But I think it is related, for it speaks about the direct result of that feeling: the fear of being ostracized, of being shunned in society for being who you are. For if there is no reason for your current treatment, what else is there but to blame your very being? If no apparent misdeed of yours caused your banishment, then it must be you yourself, no? (2)
Connected to this is the next step, which I find fascinating and which pulls us out of passive suffering to active transformation: the act of struggeling, of not accepting the hand fate has dealt us. Struggling to change your reality so that you eventually, finally will fit in and be accepted for who you are - or, on the other hand, accept yourself for what you are. (3) But a third, terrifying option remains: that you will never find acceptance. That you will always stay broken.
Here, I actually can give poetric advice: try Ocean Vuongs poetry collection "Time is a Mother" (2022). In their work, they often speak about the struggle of coping with life and of trying to fit. Especially their poem "Beautiful Short Loser" brings it to a poingnant point: one person in it decides to leave the world intact via suicide, the other one needs masectomy to feel more whole. I wish not to quote parts of the poem, for it would not make sense to take the pieces out of the whole. Therefore, I linked the poem here. Go forth and experience it yourself.
Seek heaven through violence.
(1) Granted - it is not a poem, but a novel. But knowing Mr. Murakamis style
of writing, I often ask myself - what is the difference? If a poem is
written to make us feel something the author felt, then the works of him
definitely fulfill that role - but I digress.
(2) At least this is how I feel it. I cannot speak for Baudelaire and his
poem - I do not speak French and the translations of the "Spleen" I
found online were hard to read for me. But the feeling itself is deeply
familiar and haunting. What fault of mine do I not perceive if my mind
tells me that I do not fit?
(3) Strangely enough, my best example for that is the character development of Guts from Kentaro Miuras' "Berserk" (1989 - present). From the very beginning, you see him alternating with the perception of others of him as a horrific killing machine, a monster designed to slay other monsters. Only by growing into a found family he slowly can accept things for what they are and even reach some sort of mental peace with the results of his truly disturbed past.