Big caliber = big gun. If you're a big person, it's not hard to conceal it. If you're not a big person, you'll have a hard time concealing it. You should go to the range and rent some guns. You should consider some of the excellent pocket guns on the market today. Ruger LC9, Keltec PF9, SW MP Shield in 9mm.
The 9mm is plenty fine for personal defense. Lets face it, if you shoot someone in the eye with a 22LR, you'll probably kill them. A gun you can control is the key to self defense, not the caliber.
I have a Keltec PF9. I trust it, it shoots well and I can conceal it easily. No matter which gun you get, you'll want to get another one soon after purchasing it. You will need something bigger/smaller, lighter/heavier for some other purpose.