Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your pup is suddenly licking everything, sneezed a few times and vomited twice.
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.
Have you looked at her teeth and gums and on the roof of her mouth?
Has her appetite increased or decreased recently?
Dogs will often lick when they are feeling nauseous or have gastroesophageal reflux to try and settle their stomachs. If she has had a change in appetite and because she vomited along with her licking I feel that she may be nauseous.
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 she see her veterinarian for an examination and some blood tests to make sure there are no health problems behind this behavior if her licking continues.
For now in case this is related to nausea or reflux to try and settle her stomach you can try either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
Either of these will reduce stomach acid and should help settle her 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 her veterinarian at her next veterinary visit even if she improves with the acid reducers as they will likely want to run some blood tests to look for any possible developing problems.
It may also help to feed her 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, then start mixing in her regular diet and slowly convert her back.
Please let me know if you have any further questions.