Well, I'm sure not an expert nor a vet! LOL
The photos are interesting.
I'm going to tag in
@Eggcessive and
@casportpony as well, they may have better suggestions than I do.
Do you notice if there's any more spots like that on the rest of his body. Is he excessively preening or just scratching his head?
It could be scaly face mites or something like Feather (Depluming)mites, but the mucous and facial swelling is different.
Sometimes more than one issue can be going on.
Your vet is just being cautious I suppose. It must be very frustrating though.
On this one I lean toward using the SMZ-TMP instead of the Amoxicillin. I think it would be more effective.
I don't have concrete dosing info for SMZ-TMP I *think* this is correct, but Kim or Kathy may have something different.
https://www.backyardchickens.com/threads/my-babies-are-dying-bactrim-smz-tmp-dosing.356425/page-2
Just doing a bit of "brainstorming" here for when Kim/Kathy come on - IF it's Scaly Face Mites or Depluming Mites (should see evidence of Depluming Mites elsewhere, I think). Ivermectin would be what I would use. Is there any contraindications between Ivermectin and SMZ-TMP?