Hi HeatherinMI,
There is more information about dust mites and allergies and methods that can be used to control dust mite populations or other allergens that are related to mattresses in post #2 here and in post #3 here. There is also more about allergy encasements in post #2 here that may also be helpful.
I can’t think of any reason why convoluted foam would be a reason for concern in regards to asthma but the BME no longer uses convoluted foam in their polyfoam base layer anyway.
I don’t make specific recommendations but some of the better lower budget latex and latex hybrid mattress options I’m aware of are listed in posts #3 and #4 here.
Phoenix