@Brenda Parker @Bobbi Coover Yes, sneezing and coughing could be related to an allergy caused by the food they consume. But usually with an allergy to food there are more contributing symptoms, such as diarrhea, constipation etc.
More commonly, another consideration is - that many cats can have and/or develop allergies to their style/type of litter. Many litters on the market contain a lot of dust and added chemicals (such as; Sodium Bentonite and Crystalline Silica for their clumping abilities) and can cause cats (and humans) to sneeze and cough. This can often lead to allergies and respiratory issues to manifest overtime.
Other consideration is: Upper Respiratory Infections (URI) which is a cat's version of a common cold. But there are usually more symptoms involved, such as: runny eyes, nasal discharge, fatigue etc.
And sometimes this could be a reaction to the dust within the home, no matter if there is a lot or barely any. Some cats (and humans) can just have more sensitivities then others.