I don't know if this would apply in your case, but my hamster was sneezing a lot also. I made an embarrassingly small discovery after that. I found when I vacuumed my house (or hoovered for those in the UK) my hamster stopped sneezing! It was like a switch was flipped! And here I put off vacuuming because I was afraid the noise would frighten him! (and also because I don't much care for vacuuming.
)