Hi hey,
There is more about the different types of latex allergies in post #2 here but I would definitely suggest visiting a doctor or health professional so they can test you for an allergy to latex.
Since your issues appear to be related to closer or more direct contact with the latex this would seem to point to a type IV allergy (that is contact related) and if this is the case then any cover that prevents more direct contact with the latex or a mattress protector that blocks any smaller particles would probably solve the issue but since a type I allergy can be more serious … even though it is very rare … if you suspect this is what you have I would definitely pay a visit to your doctor for some tests to confirm whether you have a latex allergy and if you do which type it is.
Phoenix