@Rockhead,
As a shelter vet, I see a ****-ton of eye problems in cats.
Is Baby Sarge a kitten, or an adult cat?
We've found that triple antibiotic ophthalmic ointments like Neosporin (I'm assuming your using a Neosporin product meant for use in the eyes -- if not, stop using it immediately) -- like I was saying, we've found that triple abx ointments can be pretty irritating to kittens, and often make things worse. In younger cats we usually use a terramycin ointment or, if they're particularly young or sensitive, erythromycin. If you can't get either of these (I'm not sure if they're available OTC or not), it might be worthwhile to stop the antibiotic you're using for a few days and see if things improve. Above all else, make absolutely sure that whatever product you're putting in the eyes doesn't contain a steroid -- putting steroids in there will put the corneas at risk of ulceration, and could lead to rupture of the eye (which will have to be removed surgically, which is expensive for you and inconvenient for the cat).
Is Baby Sarge sneezing, making a lot of snot, or breathing noisily?
By far the most common reason for conjunctivitis (inflammation of the tissues surrounding the eyes) and keratitis (inflammation of the cornea) in cats is feline herpesvirus, which also usually causes upper respiratory signs. Sometimes the eyes can be bad a few days before the sneezing and snots start.
Is Baby Sarge eating all right?
Cats with upper respiratory disease often have poor appetites, which in turns makes it harder for them to fight infection. One of the reasons they don't eat like they should is that they can't smell their food, and cats don't like to eat what they can't smell. If Baby Sarge isn't eating, I'd recommend offering wet food warmed up a bit in the microwave -- warm food is much easier to smell than cold food. Wet food also will help get some fluids into the kitty, and sick kitties tend not to drink as much as they need to either.
What do Baby Sarge's eyes look like?
Inflamed conjunctiva are dramatic and uncomfortable, but any irregularities in the surface of the cornea may be suggestive of an ulcer, and ulcers on the cornea are bad (see above).
Given the circumstances of your acquiring her, I very much suspect that Baby Sarge has upper respiratory infection caused by herpesvirus. Watch out for sneezing and rattling breathing. If this is the case, here are a few things you can do:
* Feed warm canned food (see above). Food intake is a big thing. Kittens who don't eat don't tend to stay with us very long.
* Take Baby Sarge in the bathroom when you shower. The warm, moist air will help to loosen respiratory secretions so that Baby Sarge can get them out.
* Put L-lysine in her food. There's some anecdotal evidence that lysine is helpful in fighting herpesvirus infections in cats. It can be acquired at any nutritional supplement store (e.g., GNC). For a kitten, put 250 mg on food; 500 mg if she's an adult.
If there are no respiratory signs at all, it could be that there is a primary bacterial infection of the eyes. Either way, it doesn't sound like the triple antibiotic is working and may be making matters worse. I am serious about attempting to stop the ointment for a couple of days and seeing if the eyes improve at all, if you can't get your hands on a gentler product to use (that is, terramycin or, ideally, erythromycin ophthalmic ointment).
More than anything, though, I have to recommend that she see a vet. If she really can't and she continues to get worse, she really might be better off at a shelter that has the capability of offering good medical care (not all can do so, unfortunately); even in cat-saturated Wisconsin, where we've got hundreds of thousands of folks who think it's a good idea to hunt ferals, kittens are an adoptable commodity.
Sorry for the long reply, I hope it's useful to you.
Sorry, editing -- for some reason I didn't see the following posts, and I'm too lazy to go back and edit. I just want to ask --- you're absotively, posolutely sure that she's not packing a nose full of boogers?