OK. Just had to ask or mention it. People keep Turkeys for a variety of reasons from food to pets so you never know.
If she's a pet and you're not going to butcher her, then Baytril would be what I'd use.
Pus in birds does become somewhat solidified or like a semi solid that has to be removed. It won't dry up on its own even with an antibiotic.
So, removal is needed unfortunately. If you can't press it out, then the other option is to lance and remove. Kathy may have some tips or tricks for removal and recovery.
The poor thing, I'm sure it's uncomfortable. In the meantime, I'd keep her eyes cleaned with saline, apply a dab of Terramycin in the eyes. If you can get some pus out that gives her relief by warm compressing and pressing them out, then do that until you decide if lancing is appropriate. I would also have any supplies needed on hand before I started that process.