Is accepting marriage to a righteous young man who forgives a girl for her previous relationship with his uncle, but still suffers from doubts and obsessions, considered an injustice to him, or might his condition change over time?

It is permissible to accept marriage from this young man, and there is no injustice to him in that. The questioner must repent and conceal her past sins, and not disclose what she fell into of the forbidden, for it is obligatory for a Muslim to conceal their own sins if they have committed an indecency. These occurrences should serve as a lesson for every rational person to realize the ugliness of forbidden relationships, the harm of being complacent in them, and the harm of disobeying the Sharia (definition) in its command to conceal one's own sins.