Is an abscess on a cat that has undergone operation supposed to be an open wound with pus still draining?

There is no tube for the drainage, and the vet gave me no pain meds or antibiotics. I thought after cutting away dead skin they were supposed to close the wound back up. What worries me most is the sight of the wound, it stretches from right under the chin to the top of the throat. The circumference of the wound has to be at least 3 or 4 inches. Everything inside of me is telling me that this is way past the threshold of normality, granted the wound was quite a bit more massive than that before it got operated on. The abscess itself formed within the space of 2 days, and somehow had burst into her mouth, which is extremely distressing and troubling. I didn't take her to her normal vet, and I'm hoping someone with veterinary knowledge can tell me if this sounds like SOP for an abscess. It seems to me that they took away entirely too much skin, I highly doubt that much of it was necrotic. The procedure was more expensive than I have the money for, but I love this creature more than any damn amount of recycled green fibers. The only advice I was really given was to take a warm compress to the affected site twice a day for 10 - 20 minutes. They say she has a low red blood cell count and possible kidney disease. Could this be a reason for not prescribing antibiotics? They had given her an antibiotic injection, but the lack of a prescription has me worried. Now, I'm a pretty paranoid individual, but nothing about this situation feels right to me. Can anyone offer some guidance?