I got a puppy from a kill shelter. And she was fine at first. After a few days she started coughing/gagging.. And it gets worse at night. And now my 5 year old dog Rosey is coughing.. Her's is more like a barking cough. I don't know what to do.

First of all Props for adopting and giving a puppy a second chance.:)
You could very well be dealing with kennel cough or ITB given that your pup came from a shelter setting. That is just a guess on my part.
If it is in fact kennel cough they will need medications to relieve the symptoms. The only way to know for certain is a trip to the Vet.
But sooner rather than later if possible because the hacking can cause throat irritation that will deter them from eating, resulting in two pretty crappy feeling dogs.

With kennel cough, you can treat at home with relatively inexpensive meds.

Mucinex (the green bottle) has a drug in it that will help with the congestion and the coughing. The green bottle doesn't have anything else in it and works! For a pup, I would probably give half a pill and follow the directions on the box.. like if its for 12 hours or 24 hours. I also like to give raw honey. The raw honey has bacteria in it that help kill off the bad bacteria in the throat.

Kennel cough.. aka bordatella bronchiseptica (the bacteria) and ParaInfluenza (the virus) doesn't have anything that will actually "cure" it. The only meds given are antibiotics to help prevent secondary infection. You may possibly get some cough suppressents as well if you chose to go to the vet.

Kennel cough is just like the common cold. It runs its course and moves on. And it typically gets much worse before it gets better.. Just imagine you with the cold.. Just keep her warm and keep her drinking. She may pick at her food, so heat it up. Kennel cough stuffs up their nose, just like it does ours, so she won't have a big appetite due to her not being able to smell the food. Heating it up should help.

I know its scary when our dogs get sick. They can't tell us how they feel.. But kennel cough is not the end of the world.. And just because she is coughing, doesn't necessarily mean she has kennel cough itself. There are millions of strands of upper respiratory diseases.

I help my mom run a rescue. And whenever we get a dog in with the sniffles, they get musinex and raw honey. It clears up within a week.. viral or bacterial :)