There's something unusual in your story. Most swarms leave 5, 10, or even 20 queen cells. Seldom, if ever, just one. It sounds like the swarm came to your yard from a neighbor's hive. Your hives may be superceding, or replacing their queen.
If you want more hives, I would make splits. If not, I would add a box to the other one also, then move the non-brood frames to the top box other than the 2 outer frames. One on each side. Fill in with empty frames for her to lay in. Adding another box will not help if she has no empty cells to lay in in the brood nest. No cells to lay in means she WILL swarm.
Yes, the swarm can feed themselves and survive, but they can grow much faster if you will feed them some sugar water, mixed in equal amount. IE: One pint water, 1 pint sugar.
PS. Welcome to the forum.