My name is***** and I am sorry to hear that Sam is sick.
Just to clarify- his symptoms include- not eating hard food, coughing leading to blue tongue and gums, obesity (with difficulty with weight loss), swallowing hard. Does this sound right?
For blood work- has your regular vet checked his thyroid level? How about a screening test for Cushing's?
Based on your description, I would wonder about a few different things-
-I am very suspicious that his obesity could be pressing on his airways, especially when he is coughing. He could also have very soft rings of the trachea (common in small breeds and called Collapsing Trachea) and when he coughs his trachea is squished, making it very difficult for him to breathe. He may also have laryngeal paralysis, which is where he cannot open or close his voice box when breathing. When he is relaxed, he can breathe normally, but if he becomes stressed he can feel like he is choking.
-another contributing factor could be allergic airway disease. I know you mentioned this, but some dogs need some steroids in low doses to help reduce inflammation in their lungs. Typically the dose is very low, so we won't see weight gain or excessive water drinking.
The next part of this is his swallowing hard/possible reflux. Obesity can also contribute to this because the fat in the abdomen is pressing on his stomach. Also, having a low thyroid can slow stomach emptying time and cause reflux. Have you tried Pepcid? The dose is 0.5mg per pound, so I would recommend giving him 60mg twice daily and see if this helps. Pepcid is the most effective antacid available for dogs.
If we are concerned about a possible tracheal foreign body, the only real way to find it would be with an endoscope down the trachea or with a CT scan of his chest.
Does this help? Do you have any other questions?