Re: New inexperienced queen or laying worker?
it could be a new queen. It could be laying workers. From what you've said, I think the chances are good it's a new queen. Laying workers lay lots of eggs everywhere, you'll see more than two per cell and they would be scattered around all over. A new queen will contain them within an area like queens do, and sometimes at first they do lay a couple per cell. The only way to know is to see the queen, or give it time and see what develops.
I've been keeping a few hives for the past 20-25 years, and no longer treatment free as I got tired of the losses.