I'm sorry to hear that your pup Maximus is suddenly acting hyper and licking everything, followed by vomiting, and now he is licking again.
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 his teeth and gums and on the roof of his mouth?
Has his 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 he has had a change in appetite and because he is vomiting along with his licking I feel that he 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. In a young dog however these symptoms are usually due to him eating something he should not have, leading to nausea and possible gastroesophageal reflux.
I do recommend that he see a veterinarian for an examination and some blood tests to make sure there are no health problems behind this behavior if his licking and nausea continues.
For now in case this is related to nausea or reflux to try and settle his stomach you can give 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 half of a 20mg tablet per 20 to 40 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 may want to run some blood tests to look for any possible developing problems
It may also help to feed him a bland diet as well for the next few days. 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 his regular diet and slowly convert him back.
If he is trying to vomit but unable to do so, has a rapidly expanding, tight abdomen or seems uncoordinated and staggering then I recommend he see a veterinarian on an emergency basis as these can be signs of bloat, which is a life threatening condition.
Please let me know if you have any further questions.