Your pug was given a corticosteroid (prednisone) as well as hydrocodone which is an anti-tussive (cough suppressant). These are very effective in most cases.
Let me tell you a bit more about Tracheal Collapse so I can better explain treatment options....
The trachea is the windpipe that you can feel in your own neck. It is held open by rings of cartilage. Cartilage is the same stuff that your ears are made out of, and as you can tell, it is not hard like bone. The cartilage rings in the trachea can collapse in some dogs, causing the airway to suddenly narrow. The cough that happens in this situation is often described as "goose honking" or like a seal barking.
Tracheal collapse can vary from mild (only occurs very rarely, often when the dog is excited) to severe (occurs constantly, with the trachea not popping back open easily or at all).
Here are some videos of dogs with tracheal collapse:
In terms of treatment, here is my usual treatment plan:
1. The first thing I would suggest is that your pug should *never* be walked on a collar. Instead, you should get her a harness that goes around her chest. Thus, if she suddenly sees a squirrel and pulls, she is not going to put pressure on her trachea and cause it to collapse.
2. Next, if your girl is having an episode, then please have a look at her gum colour (lift her lip over her canine tooth to see her gums). Compare it to the colour it is when she is relaxed. In both cases, it should be a bubblegum pink colour. If it is blue or muddy coloured during a coughing fit, then you should make an appointment with your vet.
When your pug is having an episode, you need to calm her so that she stops gulping big breaths in, as that just keeps the trachea collapsed. What I find works with many dogs is to stand them in front of you, and lift the front legs up, so the dog's back is against your shins. Then, gently rub the belly. This seems to straighten the trachea and calm the dog and often ends the episode.
3. Keeping your dog as lean as possible will help to minimize tracheal collapse. If she is 3 years old, and this has only JUST NOW become a problem, it may be because she has put on a little bit of weight in the last year. Even 1/2 a pound can make a difference between a dog who has no episodes, and a dog who has a problem. Talk to your vet about a diet dog food that may be appropriate for your girl, and of course try to minimize treats!
4. Some dogs need to stay on low doses of prednisone and hydrocodone long-term. Hydrocodone can lead to constipation, so you may wish to start your pug on some metamucil to counteract this problem. It is usually given at 1 teaspoon per 10lbs twice to three times daily.
Here is more about these: http://www.petplace.com/drug-library/prednisone-prednisolone/page1.aspx
5. Some dogs need bronchodilators as well as prednisone and hydrocodone. This can be given as a pill, or as in inhaler to be used at times of severe attacks.
A common bronchodilator used is theophylline - http://www.petplace.com/drug-library/theophylline-theo-dur/page1.aspx
And an inhaler that might be used would be Flovent - http://www.floventdiskus.com/
6. With the most severe cases, a specialist can place a "stent" in the trachea to hold it open. This is very rare, and in 14 years of practice, I have only seen one dog that needed this!
For more information on tracheal collapse, here are a couple of links:
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Best wishes to you and your Pug!