Hello, your hen appears to be a Blackstar. I too have a Blackstar with the same symptoms. Took her to my vet, he diagnosed her with a large hernia and congestive heart.
He said it was nothing I did or she did, just happens to some breeds.
He said she could live with the hernia - but the congestive heart would be terminal. However, because she is still eating, drinking and getting around...I should take her home and let her live out her chicken days that God had set for her.
So I did. I have also opted to provide her with supportive care:
* Soak in Epsom salt bath for 10 minutes 2-3 times a week.
* Rub Preparation H or The Rub Herbal cream or Desitin Ointment on her swollen area.
* Detox in drinking water 2-3 days a week with "Lily of the Valley Aloe Vera 80 Detoxifying Formula"
* Sprinkled "Vionate Vitamin Supplement" on layer mash for 8 weeks.
* Black grapes everyday, cause she loves them!
* 1 tablespoon Meat protein 3 times a week.
* Fresh greens 5-6 days a week.
After all this she is now walking normally and scampering around the yard with her pen mates! I haven't seen her panting the way she was either.
I know it seems like a lot of stuff to do, but I love this chicken. She is my pet.
What ever you do, don't let anyone try to insert a needle to drain her abdomen. They will kill her. Just let her be.
Good luck!