No, it's not a matter of affording anything. I've kept animals all my life and grew up on a 300 acre beef and dairy farm so I'm not a newbie. If I thought this bird was seriously suffering, I would do something one way or the other. As you drew a comparison to treatment of humans, I got bitten by a horsefly this year and my hand swelled up like a balloon. It was uncomfortable and itchy but otherwise I was fine. Did I seek medical help? No, because I knew it was just a reaction and as long as I was feeling OK, it would pass, which it did.
This hen is not hunched. Her tail is up. She is strutting about, scratching, eating and drinking well. The swelling looks uncomfortable but I doubt seriously painful. If I thought she was in serious pain, of course I would take immediate action. I'm well able to kill a bird, pluck draw and pop in the freezer if required. In fact I did a RIR cockerel this morning. I also know a poorly hen when I see one and have no problem dealing with the situation if need be, whatever the value of the bird. Welfare always comes first.
The question really is whether it's healthy to have a hen prone to sickness in the flock. They were trying to eject her when we took her out and at that stage to swelling was tiny. They know it's not good to have sick birds as it puts the health of the flock at risk. Secondly, if she's having this problem again and we give her AB's is she just going to suffer again in the future. If we let her get over it will she be stronger for it? Personally I believe that AB's administered by non vets in an ad lib fashion is a hugely dangerous thing for animal and thus human health.