Sometimes you have to take skin scrapes to see what parasite it is, check your water quality as well, as bad water quality can make fish flick and rub, good luck.
It's hard enough to move from one home to another and worse to have to move fish. It's a guess, of course, but I think there is a good chance they got a little chill in the process. This is usually enough to bring on a bout of ich/whitespot.
If it is ich, it shouldn't take very long before the tiny "saltlike" spots appear. Then diagnosis will be pretty certain.