Aspirin is administered in the event of a heart attack because the heart attack involved blood clotting, which the aspirin would counteract.
I'm not up to speed regarding animals and pain killers which are safe for them, but to my knowledge aspirin is safe for chickens. In my own flock, if a chicken is ill enough to need pain medication, I'd be culling her.
She looks like there are some puncture wounds around her right shoulder and wing. Any others? Can you clean the wounds with normal saline, then apply triple antibiotic to them? I would avoid the hydrogen peroxide. It is very hard on broken skin and not recommended for wounds, other than initial cleaning. even so, saline would be better IMO. Saline can be bought in a spray bottle which can be used to irrigate the puncture wounds.