How can I handle black pepper without sneezing?
Your local hardware store or DIY shop will likely have an assortment of dust masks you could try. The simplest ones would be cheap and very quick to put on and remove, and should help.

It seems a little over the top to have to put on a mask for using pepper, but perhaps you're extra sensitive and it's just something you'll have to deal with.

Do you have any reaction at all from eating things with lots of black pepper?

Finally, you might look at how you're physically dispensing the pepper. If you're shaking it from a container you're likely to stir up a small cloud of fine pepper dust. If you're not already doing so, consider trying to use a tiny measuring spoon or even the wrong end of a regular spoon to scoop a little pepper out of the container directly and add it to your food--less sprinkling/shaking, less irritant in the air.