Southwest's stated carryon dimensions are 24 x 16 x 10 inches. My bag, as measured when I got home (before I unpacked), is 23 x 13 x 10 inches. (23.5 tall if the soft fabric handle sticks up a bit)
However, I was forced to gate check my carryon by the gate agent, who said it was too big. When held against the sizer, it obviously fit to my eye, but she was insistent that it didn't.
This same bag has been on probably a hundred Southwest flights before and never even came close to not fitting in the overhead.
Beware that even if you are group A, the truth may be stretched to force a gate check. Have all meds and batteries ready to pull.