You should be safe to put them together, just keep an eye out. If you see some older ones pecking the younger ones. They are asserting their dominance so don’t get worried. But if the pecking keeps up and gets aggressive I would bring them back down to your basemen :)
If I were you ( if you can) relocate them from that basement if possible) because even though you think you got all that dust, there’s probably still more causing them to cough and sneeze! And I would be carful, is it dark where the chicks are? Because if they don’t have enough light that can...
Where are you keeping your chicks at right now? How old are they? Where they are stored, is it clean and is it dusty in there? Send a picture of where they are staying.:p