A .22 caliber bullet has rather puny terminal ballistics and requires precise shot placement for effective results. Kill shots are to the eve socket, directly through the ear canal, or you might get lucky and sever a carotid artery if you try for the windpipe/larynx. These shots require that you be in close contact with your antagonist, hardly a proper placement for self defense.
CIA spooks and Mafia hit men like .22 firearms (I am told...) because they are small, light, easy to conceal, and relatively quiet. Their sound signature may be further reduced by fitting a small suppressor but be advised you are now entering Class III territory and need sanctions from BATFE before proceeding legally.
If your goal is to "get out'a Dodge" then a shot or two to the kneecap might slow your antagonist down or it might simply piss him off. Again, precise shot placement would be required to hit a small target like a kneecap on a moving man.
Two rounds, center of mass is a lot easier with a caliber beginning with a .4x (.40, .44, .45ACP, &c.) Self defense is far easier when you can maintain a reasonable stand off distance with your antagonist. .22 caliber rimfire weapons do not fit into this scenario. They are more fitted to targeted assassinations by Pros.
Regards,
GtG
G