Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your pup Handsome is suddenly licking and gulping and has had a vomiting episode and drooling last night.
Since this is a new behavior then dogs will often lick when they have a bad taste in their mouth but that should not last long. They can also lick when they have something caught between their teeth, an infected tooth, or something stuck on the roof of their mouth.
Dogs will often lick when they are feeling nauseous or have gastroesophageal reflux to try and settle their stomachs. Since he has vomited along with his licking I feel that he is nauseous.
This may be related to eating something he should not have (something outdoors, toy pieces), too many treats or too much table food, an abrupt diet change or swallowing a large chunk of a chew treat. Metabolic diseases that cause stomach upset like kidney or liver disease, hyperlipidemia, or pancreatitis can cause licking. Anemia can lead to pica or eating or licking non food items. I do recommend that he see his veterinarian for an examination and some blood tests to make sure there are no health problems behind this behavior if his behavior continues.
For now in case this is related to nausea or reflux to try and settle his stomach you can try either:
1) Pepcid-ac (famotidine) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours.
Either of these will reduce stomach acid and should help settle his stomach. You can use these for several days if need be or even long term as they are very safe medications.
You do want to mention this behavior to his veterinarian at his next veterinary visit even if he improves with the acid reducers as they will likely want to run some blood tests to look for any possible developing problems.
I would feed him a bland diet as well. A homemade bland diet consists of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled, white rice or pasta. Give small meals several times a day. Feed the bland diet for several days, and if he goes back to normal then start mixing in his regular diet and slowly convert him back. If his symptoms return with a return to his regular diet then discuss using a low irritant diet like Hills i/d or Purina Veterinary Diets EN with his veterinarian.
Please let me know if you have any further questions.