Dona, hello again,
Thanks for reposting this other question about Cupcake, although I'm sorry I was off my computer when you did.
We will often prescribe or suggest antihistamines such as Hydroxyzine (or I will anyway) when congestion issues are present if I think there's a post nasal drip aspect to the problem. I'll also suggest them for some skin allergies although they aren't usually strong enough to prevent itching and scratching for many patients. However, to be honest, I'm not surprised that Hydroxyzine hasn't helped much given the severity of her issues.
Snoring doesn't particularly bother me unless it impacts a dog's ability to breath...which it sounds like it might in this case.
There could be several possible explanations for this behavior especially if it's noticeable whether she's awake or asleep:
1. elongated soft palate could be responsible although this would be a problem that she was born with. It wouldn't develop acutely or suddenly in other words. A thorough inspection of the mouth is sufficient to diagnose this problem although sedation is often required to do so. Surgical correction is the treatment of choice.
2. Edema or swelling of the structures in the back of the throat can also contribute to respiratory issues as you describe. Again, a thorough exam should identify this problem but sedation would, most likely be required.
Over the counter aspirin might help to reduce inflammation. If Cupcake isn't currently taking any steroids or nsaid medication, then the dose would be 10 mgs per pound of body weight twice a day with food to avoid stomach upset.
3. Polyps or masses could also be present in the nasal passages. These will be much more difficult to diagnose without advanced imaging such as an MRI or CT scan, though.
4. Laryngeal paralysis can is another condition which I'd want to rule out. (LINK). I've seen a few dogs with this condition who only had minor changes when barking so there's a wide variety of symptoms with which a particular patient might present.
I'm sorry that I can't provide any additional over the counter drugs which might help but it sounds to me as if there may be an anatomical or structural reason for this behavior....which will require additional testing.
But, certainly the Aspirin shouldn't be harmful so I'd see if it helps at all.