Did Eru illuvatar create any other world? After all the trouble they had with Arda would he not try again elsewhere without interference?

Tolkien never wrote about other worlds related to his Legendarium. He wrote stories with unspecified settings like Farmer Giles of Ham, but it can be safely assumed these stories are part of our world, albeit a fantasy version of it.

Note that Middle-earth isn't a separate world from ours. It's supposed to be our world during a mythical time. And nobody in Middle-earth would know about other worlds to begin with.

The closest thing to another world is Aman, which was removed from the Circles of the World after the world was reshaped. Only immortals (with a few exceptions) were allowed there, so only they could sail through the Straight Road.