I just got a puppy from a local shelter. His name is Domino. He is a lab/shepard mix and about 12 weeks old now. When I first got him I took him to the vet that my future mother-in-law recommended right away to get him checked out (monday). The vet said that he was fine (what I thought was a very mild exam...he did not check his temp or do a fecal only felt around and listened to his heart. After I had to ask him about when to bring him back for the rest of his shots and such he told me.
The next evening Domino started to develop a little cough. It was very small and very infrequent. By Wednesday evening he was coughing a lot. Thursday morning I called the vet again to set up an appointment for that evening.
I got to the vet and told him that Domino had developed a cough and it was becoming very frequent and that I had to assume it was kennel cough because he is young and just came from a shelter. The vet felt his throat a little bit and told me he had tonsillitis and that he was not contagious.
Fast forwarding to Saturday....I was two hours away visiting my family having a bridal shower for me. My grandpa was watching Domino in the other room and after the shower I went to check on them. They had both fallen asleep together (aww). When I went to pick Domino up to take him outside he had become very ill. He did not want to open his eyes or stand up and he was having trouble breathing. My mom went with me to take him to the emergency vet.
The vet told me that he had a severe upper respitory infection and a little bit of kennel cough. She put Domino in a nebulizer for 20 minutes (helped clear him up a lot!) and told me to keep giving him the antibiotic (SMZ) the other vet put him on and to also give him clavamox.
His coughing and snotting (for lack of a better word) has improved but it still fairly frequent. Especially at night. He will cough and hack all night long. It is now Thursday. He doesn't have very many doses of meds left. Maybe enough for 2 or 3 days (liquid form).
I guess my question is...when should I expect the coughing and snotting to stop? He is keeping me, my fiance, and himself up all night long. The vet said he should be better in about a week and that is quickly approaching. How long does it take the meds to kick in?
Any help or advice would be appreciated

He is supposed to have a follow up appointment this weekend as advised, but I want to make him and us as comfortable as possible until then. We are doing everything advised including taking him in the bathroom with us when we shower for the steam and wiping his nose off when he snots.
Thanks in advance!