Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your pup ingested an Advil, but pleased to hear that he vomited soon after and thus may not have absorbed much.
Advil contains 200mgs of ibuprofen per pill.
At 20 pounds he is about 9kgs, so he ingested about 17.6mgs per kilogram of body weight (200mg/9kg = 22mg/kg) which is just under a toxic amount.
From the ASPCA database:
◾25-125mg per kg of body weight – symptoms include vomiting, diarrhea, abdominal pain, loss of appetite, stomach ulcers;
◾more than 175mg per kg of body weight – the above symptoms plus blood in the stools, acute kidney failure;
◾more than 400mg per kg of body weight – the above symptoms plus seizures, coma, disorientation;
◾more than 600mg per kg of body weight – death.
Given the amount he ate I don't think you need to do anything further as far as inducing vomiting again because he already vomited at least some back up, or worry about true toxicity. You might see mild gastrointestinal upset if he is especially sensitive, but that should be it.
At home now to try and decrease acid production in his stomach and lessen any possible symptoms you can give either:
1) Pepcid ac (famotidine) at 1/2 of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at 1/2 of a 10mg tablet per 10 to 20 pounds of body weight every 24 hours
These are acid reducers that are found over the counter at the drug store. They can be given for several days if needed.
If his stomach seems at all upset to decrease the symptoms you can feed him a bland diet for the next several days. A homemade bland diet is a mix of 1/3 boiled minced white skinless chicken or lean boiled hamburger and 2/3 boiled white rice mixed with some low salt chicken broth to make it easy to lap up and swallow and get in plenty of fluids. Feed small meals frequently.
Things to watch for that mean trouble include vomiting, especially blood tinged, dark, black or tarry stools, or frank blood in the stools, lack of an appetite, increased water consumption and urination. But I don't think you will see those given his weight and the amount he ate.
Please let me know if you have any further questions.