The expansion is not the kind of expansion you're thinking of. It isn't like a sphere getting bigger. It's more like every ruler in the Universe is getting smaller, so all measurements of distance stretch to be longer even though nothing "really" moved.

There is, as far as we are aware, no edge to the Universe even if it turns out not to be infinite (which current evidence suggests that it probably is). If the Universe were finite, it would be more like the surface of the Earth where you could get back to where you started after going "all the way around".