Can the moss on the grass surrounding the outside of your house in the air get into the house and make you sick?

It's theoretically possible. However, there are two important things to keep in mind here:

1. Moss needs both moisture and light to grow. In most houses, places that are reliably moist (like the inside of the toilet tank) are not light enough, and places that are reliably light (like the walls) aren't moist enough.
2. Even if it did manage to grow in the house, most people don't get sick from exposure to moss.

Perhaps you meant mold, which is a different story. It still requires moisture, but doesn't especially need light (in fact, molds generally grow better in the dark), and a lot of people are allergic to molds.