I know Ann (Wylie's Mom) had a problem not too long ago where...Marcel I think it was, was gasping for air in the middle of the night, and after much discussion, they attributed it to the down in her pillow or duvet. They're thinking, though, was that one of the tiny feather particles went up his little nose and cause a blockage and then after a bit it started getting damp making less of a blockage so he started breathing normally again. (I think I got that all right??)
I have a down coat and noticed once that Bella seemed to honk and gasp after I had her tucked inside it to keep her out of the cold. Not sure it was something similar to Ann's issue or if maybe it was an allergy

Eddie's runny eyes, etc... definitely seem to be more a sign of allergy than anything else, although I don't think an antibiotic would treat an allergy.....an antihistamine like baby Benadryl would though. It's odd to me that the antibiotic made it better and then it got worse again afterward..... Hmmm....
I know it gets super cold there, but maybe you could try using different pillows/blankets or keeping Eddie in a crate or something

overnight for a couple of nights and not giving him access to your bedroom at all to see if it truly was an allergy. I don't know how else you'd know..... People are allergic to down, so I'm sure dogs can be too. Although, most down duvets/pillows will now say "hypoallergenic", but I'm not sure what that means or whether somebody who was allergic to down would have a problem with the "hypoallergenic" kind or not??