Hi buttercupbetty,
Based on your symptoms and description it appears to me (a layman) that it’s more likely that you would be type IV but of course type 1 can be much more serious so it certainly can’t hurt. If you have any doubts I would personally get tested on the assumption that it’s better safe than sorry. They often do both tests together with the blood test first just in case it’s a type 1 allergy which could lead to a reaction with the skin test series.
I’m not Ty of course but this cover is a “membrane” type which has a pore size of 0 microns so no particles would get through it. There is a little more about allergy encasements and pore sizes in post #2 here.
The membranes wouldn’t protect against any offgassing (they are vapor permeable) and to protect against this you would need a clear polyethylene plastic cover in the range of 5 mil or thicker (clear polyethylene is non toxic) but in your case it’s the particles that are probably most important and as Ty mentioned the polyethylene would not be breathable at all and would likely cause temperature regulation issues as well as trapping any moisture in the mattress.
Phoenix