It is VERY possible for reflux to affect your breathing and not feel any burning sensation. I do not feel any burn but I do feel the acid in my esophagus. It no longer makes me choke or cough like it does my husband because I've had it for so long. My GI told me over time your body becomes numb to the pain of it.
I also have a post nasal drip. All of these things wreak havoc on breathing.
What happens is the acid refluxes back into your esophagus and hits the nerves going to your lungs. This causes your esophagus to spasm which feels like heart palps but it's not. From there your esophagus begins to tighten up which is where the "tight chest" feeling comes from. As I posted earlier it is like someone is standing on your chest and you can barely breathe.
Like you I have had to miss work, social events and cancel presentations for work. I can not even breathe well enough to take my son around the block most days.
My doctor is getting ready to put me on
Reglan to strenthen the lower sphincter. It is this sphincter which is allowing the acid to come up and do this kind of damage to my breathing. All my lung tests are normal and my CT scans show no lung damage. It is truly just an angry esophagus.
Good luck!