Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am very sorry to hear that your fellow is drooling excessively and has a runny nose today.
Drooling can be a sign of nausea but it can also be a sign of oral pain due to an infected tooth or a foreign body caught between his teeth, on the roof of his mouth or in the back of his throat. Sometimes it is a sign of an oral tumor. It sounds like you have checked his mouth pretty thoroughly and there isn't anything there that would cause his symptoms.
Drooling and a runny nose can also be a response to eating a bitter bug or plant piece, or smelling/tasting something especially noxious. If these symptoms came along with facial swelling or hives it could be related to an allergic reaction.
I do recommend rinsing out his mouth with cool water several times. If you have saline nasal spray you can use that to try to flush out his nose.
I know that may have you looked in his mouth but sometimes it takes a very close look under sedation to find the problem. If he will let you examine the inside his mouth again closely for swelling, reddened areas or any sign or trauma or a foreign body.
Something that you may not necessarily see, but could cause these symptoms would be a penetrating foreign body (bone splinter, thorn, wood splinter) entering through the mouth and either penetrating or getting very close to entering, the nose or sinuses or something getting stuck up above his soft palate.
You can give him acid reducers to try and settle his stomach in case this is related to nausea. Either:
1) Pepcid-ac (famotidine) at a dose of one half of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at one quarter of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle his stomach. These are quite safe and can be used for several days if necessary.
A couple hours after one of the acid reducers is given you can offer small amounts of water or ice cubes to lick.
If that goes well then late today or tomorrow start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 plain, boiled, white rice. 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 over a period of 5 to 7 days.
If he attempting to vomit but unable to do so, or he won't lay down and settle or he is pawing at his mouth or unable to drink water normally then I recommend he see a veterinarian immediately as these can be a sign of something stuck in his mouth or the back of his nasopharynx, up above his soft palate so you cannot see it.
If his drooling continues in spite of using an acid reducer and a bland diet then he should see his veterinarian for an examination, some blood tests to look for underlying metabolic disease, possibly sedation to look closely in his mouth, up behind his soft palate, and take dental radiographs.
Please let me know if you have any further questions.