Excessive saliva and gulping and licking his mouth are signs of mouth pain, nausea or sometimes a seizure. Check your dog’s mouth for tartar on the teeth, possibly red gums, darkened teeth, broken teeth or something caught between the teeth or gums. If you find something stuck, try and remove it. If it is bad teeth, you can give her Buffered aspirin can be given to a dog with a dosage of up to 5 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet.
Check just under your dog’s jawbone for a swelling and under your dog’s tongue for a swelling. This is where some of your dog’s salivary glands are located. If you find a swelling here, it’s possible your dog has an accumulation of fluid near the salivary gland called a sialocele which is causing your dog to salivate more. This condition does require your dog to be seen as soon as possible. You can read about it here:
If you suspect it may be due to nausea you can try some Pepcid or Tagamet or Zantac.
You can read about dose amounts (and cautions) scrolling down on the pages here
If your dog becomes uncomfortable, you should take her into the vet.
If it is possible that your dog ate something toxic such as chocolate, cocoa mulch, antifreeze, medications they will need to see a vet immediately.
You can read more about excessive salivation on the following website:
Since she also shows symptoms of an upper respiratory illness, I would have her seen by your Vet. A cough like you describe could be a symptom of an infection or a more serious heart condition such as heartworms if your dog is not on heartworm preventative. I am including sites with information on kennel cough and canine influenza as well for you to read.
To help your dog breathe easier, Robitussin DM at a 1/4 teaspoon per 5 pounds can be used to control the cough. Dosages can be obtained at this website. http://www.petplace.com/drug-library/dextromethorphan-robitussin-dm/page1.aspx
I would have her seen for the cough even if you do find that the drooling is due to a mouth problem.
I hope you find this information helpful.