I've not researched this for myself, but my acupuncturist recommended against foam mattresses bc of off-gassing... this may explain the sneezing:
Mattresses that off-gas can expose you to harmful chemicals while you sleep. Polyurethane foam mattresses release a compound called toluene. In small concentrations, this neurotoxin can cause respiratory difficulties and headaches. Nonlatex mattresses are often treated with PBDEs, or polybrominated diphenyl ethers. These chemicals act as fire retardants. In high enough concentrations, they can disrupt the function of hormones in the body and can have negative effects on fertility.