Would I qualify for disability? What would my life look like?

I am in my mid twenties and have been struggling with passive fecal incontinence. I work a full time job and continue to show up every day despite the severe shame and trauma associated with my condition.
I currently live with my family, but they are strongly encouraging me to move out on my own. If I were to qualify for disability benefits, I would have nowhere to stay, and finding housing would be more difficult due to my condition.
At work, I very often offend coworkers and customers, but I always apologize and explain that it is a medical condition. The trauma is so intense at times that I experience nightmares daily.
I would like to know what options are available to me. Is this something I will simply have to live with while continuing to work full time in a state of constant shame and embarrassment, or is there something to improve my situation?

I feel like there’s really no support for something like this.