What you describe does indeed suggest gastroesophageal reflux disease (GERD)-induced asthma and also, GERD as a possible cause of your chest pain.
You should ask the endoscopist/gastroenterologist what is the cause of the esophageal ulcers, if not GERD. You might also ask how reliable is visual observation, in determining if there is or is not lower esophageal sphincter (LES) weakness. Given the ulcers, you might want to ask about a pH probe to assess reflux.
The diagnosis of mild asthma, based on spirometry, does not explain your constant shortness of breath. You should ask the pulmonologist, who apparently agreed with this conclusion, what other lung diseases or laryngeal dysfunction could cause your persistent shortness of breath, for example recurrent pulmonary emboli that are clots to the lung in which case the asthma, esophageal ulcer and suspicion of GERD could be "red herrings." Pulmonary emboli can cause wheezing and the diagnosis should actively be ruled out.
As for surgical procedures to relieve asthma symptoms, you may have heard of bronchial thermoplasty as a semi-surgical treatment of asthma. That is legitimate when all other therapeutic options have been exhausted, but other surgical therapies are absolutely not! Do not agree to this or any other non-pharmacologic, surgical therapy.
The therapy for your asthma, confusing or not to your pulmonologist, should be optimally treated until your baseline pulmonary function is normal.
You may want to seek a second pulmonologist opinion. You may need an exercise study. Finally, heart disease could be contributing to your shortness of breath. Your doctors should make sure that your heart is working normally.
I also wanted to add I was experiencing these symptoms since I had my baby in July 07