I had a feeling it was going to be the cheesy kind. I had a horse with a similarly sized swelling on the inside of its lower eyelid. There was a hole in it already when I noticed, but being all cheesy, it didn't come out. And as it was so close to the eye, I didn't dare cut it out myself, so I went to the vet.
At first, the vet thought it was a tumor of some kind - she didn't recognize it as pus at all, before it started flaking off as she touched it. Even though I'd already told her that was what it was.. Anyway, the evil vet dug the entire mass out piece by piece through the already present and way too small hole, with her FINGER, without any kind of sedation. And my poor horse did nothing but trying to turn his head away. What a trooper.
I was thinking she was going to cause a huge amount of tissue damage, doing it like that - expanding the hole with her finger - but she gave us some antibiotic ointment intended for cows with mastitis to put in the hole every day for the next week but after two days there was no swelling left so we couldn't even get to the hole at the inside of the eyelid to apply the antibiotics.