Looking at your other threads I don't see any prolapsed tissue.
Could it be that she's trying to push out lash material?
You mention she's pushing out pus - can you get a clear photo of that the next time it happens?
Hard to know what's going on with your girl. Again, looking at your other threads, this has been going on for a little while.
I would agree that she is likely suffering from a reproductive disorder. Sometimes there can be fluid in the abdomen that makes them have a hard time breathing or she may simply be failing and this is the cause of the gasping for air.
Do check her crop to see that it's emptying overnight. Make her comfortable as you can and see if she will take some fluids.
No one can tell you whether it's time for her to go. You are her keeper and seeing her first hand, so it's up to you to make that decision. If you feel that she's suffering greatly and/or is in pain, then putting her out of her misery is a kindness.