Child Has Headaches Trouble Breathing

My 4 year old has been having trouble breathing for a month. He complains of headaches sometimes but the main symptom is his breathing
.....he just keeps taking a very deep breath, then stops breathing and follows with another deep breath. He has a hard time talking because he gets short of breath. None of the doctors he has seen thinks it is asthma or allergies.
He has seen a cardiologist and an ENT to no avail, their tests were normal. They have done X-rays, an EKG, and various blood testing but have come up with nothing. He is also type 1 diabetic and ketoacidosis is negative.
The dr tried singulair and claritin, but nothing is helping. He does not have any wheezing or cough, just the shortness of breath. I don't know if it is pulmonary, gastric, or neurologic problem. The dr will not refer him to another specialist and says to "ignore" that he has breathing difficulty!