Golden, the maximum size for a carryon bag is 22 L x 14 W x 9 D. Carryon bags come shallow enough, so when they are expanded, they must be checked. The length of that bag is irrelevant because you said it is only 21 inches long.
I don't care how small a bag is; I am going to check it every time. Years ago I flagged a TSA agent by not putting my suitcase on the x-ray belt. Ever since, my family has only carried on luggage that way when we flew to Gainesville's regional airport, which has no Southwest gates, and back home from there.