So, if space wraps round like you described, and if the universe is constantly expanding, isn't the universe one day going to have to stop ?
Not necessarily. If you carry on blowing up a balloon, it just gets bigger and bigger, indefinitely. The surface of the ballon is like space. Imagine the balloon has lots of bits of stuff stuck onto it, like grains of sand. They are like the galaxies in the universe. As the ballon expands, the grains of sand get further and further apart. As the universe expands, the galaxies get further apart.
Also, earth has a limited size and it is inside space, which also had a limited size, so what is space inside of ?
The balloon is a two-dimensional surface curved around within a three-dimensional space. The universe is a three-dimensional surface curved around a four-dimensional hypershere. Elsewhere, unknown to the grains of sand on the balloon, there may be an entirely different balloon somewhere else in the same space. There may be other universes in a higher dimension of space. One theory is that the universe is only one "bubble" in a boiling froth of millions of other bubbles. Each one is a different universe, and they make up a multiverse. Some of the individual bubbles within the froth may last a long time; others may pop or combine with each other.