My Pill Book Guide to Medications for Your Dog and Cat says:
6.25 mg/lb twice a day. So that's a high dose.
Before you are completely sure that "rapid breathing" is a medicine side effect tho, be cautious. If YOU are concerned, and are looking at the dog a lot, the dog is liable to be a bit worried. This IS a puppy and they only have two speeds -- RACING and z-z-z-z-z-z-z-z.
What I'm saying is, a dog with kennel cough is going to have a hard time with respiration anyway -- the rapid breathing MIGHT simply be a side effect more of the illness than anything else. I'm not saying you're wrong -- but it would be extremely unusual for two drugs to cause the*same* symptoms. Rapid breathing is way way down on the potential side effects of this one.
With the dose as high as it is, I'd expect vomiting or diarreha. NOT a lesser-known symptom first.
Also according to the Pill Book diarreha and vomiting are the two biggest signs of over-dose.
Realize -- a vet can and often WILL exceed common drug guidelines and the vet may feel it's warranted since this has gone on so long. Clavamox is a pennicillin derivative, and typically thot of as very well tolerated.
The risk here is that in order to pacify you (and I"m not being nasty -- but very often vets will prescribe more to satisfy the owner than what the dog needs, if they think they have to in order to keep peace or keep the owner happy) you may wind up skipping to another drug too quickly.
It typically takes way more than a week's worth of an antibiotic to get rid of kennel cough. It's like bronchitis for humans -- it can linger and a puppy who has had it since it was a wee thing has all the stress of the body growing SO rapidly at the same time it's trying to get well. That 'stress' of simply being a puppy makes the immune system fragile, and it's at a time when the immune system is weak anyway.
What else has the vet given -- when you "stopped all the meds" what was the dog taking?
I'm surprised the vet was using hydrocodone -- now THAT could cause you to breathe fast -- it's got codeine in it -- it's a narcotic cough supressant (and not really often given to dogs).
There are other things you can use as a cough supressant -- honey and lemon works very well, and if you use fresh lemon it's good Vit C.
Now, I'm not defending pharmaceuticals -- I would likely encourage you to use gentler things -- and, in fact, it might be a good time to look at other vets unless you are really sold on this one. It seems like this vet is using pretty strong stuff, and if you are right, this dog might not be tolerating it well.
I'm not trying to give you mixed signals here -- first off, YOU are the only one there with your dog, so you are ultimately the one who will know how the dog is reacting to things. But it's easy when you have a sick baby to get SO worried and worked up about "stuff" that everything you give them is a cause for you to worry and that's not good.
Some things to boost this baby's immune system would likely be a good idea -- there are a good many benign things like colostrum (1000 mg twice a day), Vit C (125 mg about 4 times a day if it's well tolerated). A good supplement like Solid Gold's Sea Meal (which is formulated for skin and immune system) just added to the dog's food might be a super good thing to help build the immune system.
If you want to try honey and lemon -- it's easy. I like raw honey, but any honey will do. And just add lemon to thin it to syrup consistency. Additionally you can add some water and then slippery elm powder -- that's also going to soothe the bronchial passages and the stomach. When slippery elm is mixed with water it becomes a gelatenous mess -- so just again thin it to syrup consistency.
With honey and lemon and slippery elm, there is no real 'dose' -- pretty much you can use it as needed.
These aren't curealls -- but just helps.