Diagnosing Kennel Cough or a Collapsing Trachea really should be done by a professional. I would take him to the vet for his first visit and check up (most breeders require you do this in the first week you bring him home anyways).
The vet can diagnose him and hopefully help your little one out.
Bordetella (kennel cough) can be treated very easily with an antibiotic called Calvamox.
If it turns out not to be Bordetella or a collapsing trach you can look into using a dog water bottle. Toy breeds sometimes have issues where their trachea and esophagus are very close together (this is usually directly correlated the the length of the dogs neck--the shorter the neck the more prone they are). When they drink from a bowl on the ground this can cause water to go down the trachea instead of the esophagus, where it should go. Sometimes you will hear them snort/cough to try to clear the water out of their lungs.
Overtime, all of this water can build up in the lungs and cause phenumonia.
The safest way to provide water to a small dog is through a water bottle (almost like a rabbit bottle) that are specially designed for dogs. The spout is larger than say a rabbit feeder. Training your dog to use it is very simple too.
Here is a link to the bottle I use:
http://www.petco.com/product/6140/Li...r-Bottles.aspx
My moms Yorkie suffers from a collapsing trachea and was diagnosed when she was only 10mos old. This can be triggered by pressure on the trachea by collars and some harnesses. Depending on the severity even exercise can trigger them to cough very loudly. They sell special harnesses that are shaped like the outline of sunglasses that wrap around the dogs midsection and go thru the front arms as not to put any pressure around the neck area.
I hope this helps!