Ooof!
Yes, definitely use your gloves for the neosporin, etc.
When I read this, I thought - o.k. Colloidal Silver. I do not know much at all about alternative treatments/methods, but do know that some use it. I also knew @Hen Pen Jem and Coach723 both have written about its use. Looking at some of their posts, they still seem to recommend using it in conjunction with "something else" like neosporin, etc., instead of alone. It would be a complimentary type of treatment I suppose. The best thread I've found where both of these ladies have given info is this one https://www.backyardchickens.com/threads/colloidal-silver-dosage.1277070/
But if you search colloidal silver and put in the username you'll find numerous other threads. Hen Pen Jem hasn't been on since January, so, but she always had good info. Coach is active is you wish to reach out to her, I'm sure she'll give you her support and suggestions.
I had thought about separation too, but if Tamar is getting on o.k. and eating/drinking, not getting picked at, then personally I'd leave her for now. You're right, it's hot and humid, separation even within the run/coop can be stressful and since she's low in order may not fare as well being separated as say a top hen or rooster.
BUT!! If you do speak with your vet and get any type of antibiotic to give orally/by injection, etc. You probably need to separate her to collect her eggs so you can toss them unless you know without a shadow of doubt which egg is hers - but with you being allergic to all antibiotics, you do not want to eat her eggs period for a good while. Depending on which antibiotic, the throw away period may be from 14 days after last dose on up to 75 or so. Not all antibiotics have been studied (takes funds) to get an "official" withdrawal period. Most medications exit the body fairly quickly - but with an allergy, you want to be very cautious. I can't do Sulfa drugs, so oh boy, I avoid that, but if I had to use them for a hen, then I'd toss those eggs for a few months - just sayin'.
Do the best you can. The wound doesn't look infected from what I see in the photos. You don't detect an odor. She's eating/drinking and interacting but still limiting some activity but that's normal with an injury.
An injury like this is concerning, it can be hard to know which way it will go. She may heal up beautifully in time with daily care like you are doing - seems like she's holding her own for now. There's a worry that it could take a bad turn, so this is why I ask about meds to have on hand just in case, but they may not be needed.
