Bike sizing is a bit of art and bit of black magic. You need to know basically your height and real inseam, this is your inseam barefoot from the ground to your junk and is usually a couple of inches longer than your pants inseam. It sounds odd (and what about cycling doesn't really), but you stand with your back to the wall, feet a few inches apart and bring a paperback book just until it touches your crouch. The distance from the top of the book to the ground is your real inseam. Your torso length and arm length will also factor into the right size. There is actually a pseudo-medical term for it, pubic bone height and you'll sometimes see people refer to the PBH, which is carry-over from the Fit Kit (the tool bike shops use to fit you) terms.
I am 6'0", 35.5" inseam (I wear 34" pants usually), pretty typical reach. I ride a 58cm road bike and usually large MTB, which tends to be 19"~20". I like a bike with a around a 24.5" top tube length and look for no less than 32~33" stand over for a MTB or CX (it's often more than that, standover more like 31" or 32"). I tend to have around a 90mm stem with 5 degree of rise, 20mm of spacers.
But the magic part is that almost all bikes now have sloping top tubes, so their actual measurement is not their sizing measurement. Going way, way back the center of the bottom bracket to the top tube was typically how a bike was measured since they had flat top tubes. Some times the measurement was to the middle of the TT and sometimes to the top of the TT. Occasionally it was to the top of the seat collar. Now when the TT slopes, the BB to TT might measure something like 55cm on a 58cm size frame.
The effective seat tube length is the term they use now, since the BB to TT length is virtual. It is measured using a level held at the top tube and head tube junction to find a point on the seatpost that translates to the old 'flat' to tube point. Then measure from that point to the BB to find the sizing seat tube length.
A 22" frame would be much too tall for you. I think a 56cm might be on the small side of fitting you, but it might be uncomfortably short. You tweak the fit with stem length, stem height and saddle position mostly, but if a frame is too small or large it's hard to fit. From your description I'd think 56, 57 and maybe 58 should be on your radar or 17, 18 or 19". They use metric for road bikes and cyclocross, imperial for MTBs. Just tradition. In any case they might also be marked medium or large depending on the manufacturer. I ride large frames and sometimes XL, but I don't like being cranked at all.