Did the vet tell you this was a cyst? If they did, and then prescribed an antibiotic and anti-inflammatory for it, that doesn't make any sense. And yes, a cyst can often be liberated with a "flick" of a scalpel. Just had one of those removed a few weeks ago on myself.
The eye has more of the look of sinus infection to me. I would ask the high priced vet for a prescription for prednisone eye drops. I've used this to successfully treat such eye swelling as your rooster has. You need a prescription for it.
https://www.kvsupply.com/item/prednisolone-acetate-ophthalmic-suspension/497024/