Hi C.,
My daughter (now ten) had a lot of trouble breathing at night when she was a baby. The pediatrician suggested it was allergies, and told us to keep the pets out of her room and possibly get rid of all her stuffed animals. We tried cleaning her toys and keeping the dog and cat out, and used a vaporizer but nothing really helped. I hated using the vaporizer because it also made a lot of condensation on the windows and my woodwork started getting moldy-- which can't be very healthy either. She would snore and gasp for air at night and I was always worried about her being able to breathe.
When all her teeth were grown in and she visited the dentist, the dentist discovered she had serious misalignment of her teeth (a cross bite) and recommended we see an orthodontist. The orthodontist discovered that the roof of her mouth was abnormally arched, so the shape of her upper jaw was causing the teeth not to line up correctly. At about 6 and a half she had to wear a palate expander device in her mouth that reshaped the roof of her mouth (palate).
The orthodontist said also that doing so may alleviate her breathing problems... and it did! The shape of the palate was actually interfering with her nasal passages. Just something you might want to ask the pediatrician about or see an orthodontist. It's not as scary as it sounds, in fact it is fairly common. Once my daughter's palate was fixed, she no longer snores or gasps in her sleep. And we didn't have to get rid of the pets or the stuffed animals!
Hope this helps!
C.