If the bag can be placed in the OHSB wheels first and the hatch closed, then the bag is small enough.

I've always avoided using terms like 22" - I think of 2 x 105cm for domestic and 1 x 115 cm for international as this is what Qantas define.

A 22" bag would still be ok if the sum of it's linear dimensions (L+W+H) does not exceed 105cm (41").

In any case I don't believe the OP will have any issues with size ...