Is a Shield a Good Long Term Solution?

The sun would be pushing us outwards, but that wouldn't necessarily is in a stable orbit. Things that are further out actually travel more slowly than things that are close up. But you're right that we need to adjust the earth's velocity. We can't just like, give the earth a push and then hope that it ends up in a stable configuration. Most likely that leads to earth like drifting out of the solar system and becoming a rogue planet - which would be bad. It would take some really careful sort of solar system engineering to get earth in the right place, in another orbit, at the right velocity.