The symptoms that you describe seem to describe feline herpes (also known as FHV-1). The ASPCA lists symptoms of a feline herpes infection as
- Sneezing “attacks”
- Discharge from the nose and eyes
- Conjunctivitis or pink eye (inflammation of the eyelid)
- Lesions in and around the eyes
- Eye ulcers
- Loss of appetite
While most cats can suppress the infection once their immune system learns it, a few cats are never able to fully rid themselves of the symptoms of feline herpes. One of my four has daily sneezing and nasal discharge from it. Otherwise he's fine and lives a normal life, we just sometimes wipe his nose (and our walls).
Even though I'm not a vet, feline herpes is extremely common in rescued cats, so it's a reasonable suspicion. Your vet probably sees this problem daily and didn't take the time to explain it. I don't have a particularly good feeling about a veterinarian that doesn't realize as common as it is to THEM, it's new to YOU.
I also check with my vet regularly (once a year or so) to see if there are any new treatments for feline herpes, so that's another thing you can do. There are a few treatments that are being researched, but there is not any evidence that they work yet.
Probiotics. There isn't any evidence either way that this works, but it doesn't hurt and can be helpful if there are also gastrointestinal issues.
L-Lysine. Again, the evidence at this point is conflicting but it is made into treats and palatable pastes so you can try it without any harm to your cat.
Most of the current treatments focus on managing symptoms.
My vet recommends saline nasal drops (example, commonly marketed for children/babies). Any drops you use should NOT contain any medications without the advice of your veterinarian.
You can keep your cat in a steamy area (like the bathroom while you take a shower, or a large carrier near a humidifier) to help break up the mucous.
If your cat develops a secondary infection, antibiotics can be helpful (talk to your vet).
Keeping your cat hydrated is important (the mucous will be thinner and easier to deal with). Consider switching to wet food if you feed dry.
Additionally, make sure that you monitor your cat's food intake. If your cat cannot smell her food, she may not want to eat it. You can heat wet food for a few seconds in the microwave or add smelly tuna juice to it to increase palatability. If she doesn't eat for a few days she can become seriously ill.
Sidenote: Corneal Ulceration
One of the most damaging affects from feline herpes is the development of eye ulcers. Cornell University gives the symptoms of a eye ulcer:
The clinical signs of corneal ulceration include inflammation of the tissue surrounding the cornea; seepage of discharge from the eye; clouding of the cornea; and apparent hypersensitivity to bright light. An affected cat may squint, rub its eyes, and behave as if it is having vision problems.
If you notice these signs in the future, you should take your cat back to the vet to be evaluated for an ulcer. While most ulcers will heal on their own, they can cause severe discomfort and in rare cases can permanently affect the cat's vision.