That just makes me so sad my chickens are my friends and my family is so attached to them.
She is young. I wouldn't give up.
If you have the time to keep on top of it, well, that worked for me. Maybe I was lucky, but your hen is young so I think it is worth trying...
My Silver Gray Dorking is 4 yrs old and she didn't stop laying while I dealt with her prolapse.
I started with a soak in warm water and Epsom Salts to clean area, checked for shell, etc. Gently pat feather areas dry. With oil (vitamin E, mineral oil, etc) on my fingers, I put gentle downward pressure on the vent flap. If this prompted her to suck in the prolapse, great! (If it goes in, try holding it in gently for 10, 15, 20 min)- But if not: Spread the prolapse with honey and some sprinkled sugar. Put her in a covered crate with some towels for her to sit on and access to water. Don't feed her chicken feed - you don't want her to have enough nutrition to lay. I gave canned corn or chopped boiled egg with calcium citrate (or crushed tums). I kept her in a crate in a dark room 16 hrs a day so she would stop laying (she didn't). Every 2 hours or so I would check the prolapse, using a soft damp cloth to gently blot away any poop and then adding a fresh coating of honey or sugar. I tried to very gently apply downward pressure from the vent flap, downward - sometimes it felt she was sucking it in (in response to the pressure), and if it went in, I would hold it in as long as the hen allowed. This went on for several days. After a few days, the prolapse stayed in on its own, until she would lay and the prolapse would come out. However, after about the third day of this routine, she laid and the prolapse stayed in.
I think it's important to:
Keep the prolapse moist (I used vitamin E squeezed out of capsules)
Keep the prolapse clean (gentle, gentle blotting with a wet paper towel)
Apply gentle downward pressure above and downward over the vent flap. If she resists, don't insist.
If you have the time, check her every few hours, blot gently to clean, apply the vitamin E/oil, downward pressure, and hold it in if allowed. Before leaving, put apply honey/sugar.
In the morning I gave a quick warm soak to remove poop from feather areas. Towel and blow-dry and start with the Vitamin E.
Lather. Rinse. Repeat. Yes, it's a process. I work at home so I was lucky to be here. Your mileage may vary.
Good luck!