My name is***** and I am sorry to hear that Pickering is so sick.
First, just to confirm, are you giving him human Advil or a dog NSAID that is similar (like rimadyl or deramaxx)?
Panting is a sign of discomfort and pain, so I would worry that he is painful.
Vomiting/gagging can be caused by numerous different things-
-blockage of the intestines
-metabolic problem like kidney disease or liver disease (both of which can be caused by advil, but not the dog products)
-stomach ulcers (again, from advil)
-tumor in the stomach or intestines
Pickering needs to see his vet first thing in the morning for an exam, blood work and x-rays. Abdominal ultrasound may also be helpful.
Does this help? What other questions do you have?