Jordan:
If the bees stay in your swarm catch hive, they likely have a queen. If they don't have a queen and you put in a couple frames with capped brood, larvae, and eggs, they will attempt to make a queen by making queen cells. You should inspect the captured hive in 3 days to see if you have eggs. If you do, there is a queen. If you don't, no queen. You can buy and put in a queen.
You should inspect the hive that swarmed in 4 days. If the queen left, you will likely find multiple capped queen cells indicating they are making a new queen.
Let us know what you find on inspections and we might be able to help you.