Hi agent2440. I'm a new shooter also, and also have a P22 with the short barrel. In my first three months I've learned all sorts of wrong things that I'm doing that cause me to consistently strike the target in one area or another. If you Google for "Target Pistol Shot Analysis", you'll find a link to
http://www.targetshooting.ca/docs/Pistol_Shot_Analysis.pdf that will tell you that hitting down and to the left of center may be caused by a pull on the trigger by a right-handed shooter that exerts a slight downward pressure instead of straight back. My personal failing is to hit down-and-right, which may be caused by "pulling on trigger; snatching; anticipating." I'd suggest that, especially because you say your are just getting into shooting pistols, the problems you are experiencing at the range may be more in your technique rather than in the gun. Indeed, compensating for this by adjusting the gun will not only keep you from fixing your technique, but it will also only work as long as everything in your technique remains the same.
Although it's possible that the fault is in the pistol, as a beginner (like myself), it seems more likely it might be your technique. That's what I've discovered, and where I continue to work.
Here's the litany I try to use when I go shooting:
Grip the gun high so the impulse drives it as straight back as possible;
Position my right finger off the trigger temporarily, and wrap my left hand around the right with my left forefinger on the front of the trigger guard (this gave me a significant improvement in getting rid of the down-right tendency);
Move my right forefinger onto the trigger and touching the trigger in the top-to-bottom and left-to-right midpoint, and with the middle of the pad of that finger;
Align the sights using my right eye, and focus on the rear sight, not the target but keep my left eye open -- this can be challenging as you'll now "see" two targets -- keep the sights aligned and aim for the target on the right (squint or momentarily close your left, non-aiming eye if you're not sure what you're aiming at to verify the aim);
Hold that aim on the target [Hah! This is really tough -- I wiggle all over the place -- "practice, practice, practice" is the advice I hear];
Take a breath, let out about 50% and gently hold your breath;
Start tightening (pulling) the trigger finger and focus on pulling straight back -- when the shot fires, you should be surprised -- if you're pulling fast enough to know when the gun will fire, then you're pulling too fast (I was told). The shot should be a surprise when it does off.
That's a lot to remember but, for me, this makes a BIG difference. My groups are still much bigger than the expert shooters around me but they are also a far sight (no pun intended) better than what I was getting a month ago.
From one beginner to another, Good Luck!