I've read a fanfiction where Otabek helps Yurio overcome an injury and in the process, they realize their feelings for each other. It was really heartwarming. You might find similar stories by using specific search terms like 'Otabek x Yurio recovery fanfiction' or 'Otabek x Yurio emotional journey fanfiction' in your search on the various fanfiction platforms.
One great place to start looking for Otabek x Yurio fanfiction is Archive of Our Own (AO3). There are numerous stories there with different themes and styles. Some might focus on their friendship evolving into a deeper relationship over the course of their skating careers. Another option could be FanFiction.net, though the selection and quality can vary more widely.