Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that you gave your pup an Aleve.
Aleve contains naporoxen, which is a nonsteroidal anti-inflammatory that we do not use in dogs due to the high incidence of side effects including gastrointestinal bleeding, ulcers (sometimes perforating) and kidney damage even when given appropriate doses.
The dose listed in Plumb's Veterinary Drug handbook in 2mg per kilogram (2.2 pounds) of body weight every 48 hours.
A usual Aleve tablet is 220mgs. In a dog his size (15 pounds = 6.81kg) a usual dose would be 13.6mg, so he was given a dose that was roughly sixteen times a normal dose if he was given one 220mg tablet.
A single (meaning given all at once) toxic dose of Aleve in dogs is 35mg/kg, or 238mg (6.81kgs X 35mg/kg = 238mgs) or a little more than one tablet of the 220mg size for a 15 pound dog. So he was given a very close to toxic dose.
Peak blood levels are within 3 hours of ingestion so these levels should have occurred the first night and would have explained his vomiting after that first dose.
Toxic side effects are abdominal pain, vomiting, gastrointestinal ulcers which can perforate, dark tarry stools, weakness, anemia, and kidney damage shown by increased kidney waste product levels (BUN and creatinine) on blood testing.
Unfortunately the half life (the amount of drug metabolized and decreased by half) in dogs is very long, 72 hours, and as such the effects of the drug linger. That would explain why he has continued to vomit.
Ideally he would see a veterinarian.
Your veterinarian will examine him, look for blood in his stools and urine, test his kidney waste blood levels and urine for signs of kidney damage and get him started on sucralfate which is an ulcer coating drug, as well as an acid reducer such as famotidine or omeprazole. They may want to put him on intravenous fluid therapy to flush out any remaining drug and support his kidney function. If he is continuing to vomit they can give him injectable anti-nausea drugs.
They will also likely recommend feeding a very bland diet.
At home now you can start either:
1) Pepcid-ac (famotidine) at 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 should be given for at least 2-3 weeks, as it takes that long for gastrointestinal ulcers/irritation to heal.
Then feed bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled white rice. Give small meals several times a day. Feed the bland diet for several days, then if he stops vomiting start mixing in his regular diet and slowly convert him back.
Best of luck with your fellow, let me know if you have any further questions.