Why is my dog panting excessively, passing gas, and short of breath?

Excessive panting can be a sign of overheating, but also a sign of pain, or an endocrine disease such as Cushing's disease, especially in an old dog like yours, Arthritis is high on the list, as at that age your dog will definitely have arthritic changes that can be highly painful. Cushing;s disease is also on the list, especially if your dog developed a pot belly, drinks and urinates more than usual, pants heavily even when it is not hot, and maybe loses some hair. Both of these conditions need to be checked out by your veterinarian, in order to ensure a good quality of life for your dog. Arthritis pain can be treated well with a medication called Carprofen and/or other pain medications. Cushings symptoms can be treated with special medication that reduces the production of cortisone. A blood test can rule out Cushing's disease. I suggest you schedule an exam with your vet.