Triple antibiotic ointment is o.k., but it's not going to reduce swelling.I wash her back end, & tissue with plain cold water, & have been applying Triple Antibiotic ointment to it to keep it moist.
No, I don't have anti-inflammatory cream, since I'm not sure what to use on chickens.
I have coconut oil.
You can use an anti-inflammatory cream instead, this can help reduce swelling. Some folks use Witch Hazel, but then you will want to apply an oil/ointment to keep the tissue moist.
If you can, get some epsom salts, add those to a warm bath, then let her soak in it. I use a small tote or plastic dish pan for soaking - this can be done outside.
For me, generic brands work fine, I usually hit the Dollar stores - sometimes you can score at the Dollar Tree, if not, then Dollar General most of the time has those supplies.