Ok, first, I am about the last person to suggest things here, but I am both new to guns and I used to have a M&P Full Size 9, so I feel for ya. But take this all with a few pounds of salt, coming from a pretty much noobie.
Before commenting, I would suggest you get someone else to shoot your pistol, just to make sure there isn't something wierd going on with the gun. If you can't do that, you might try shooting it off a rest. You just want to make sure it's sighted in.
I started a training journal, basically entitled what you are saying you have, i.e. why do I shoot low and left (but I'm a lefty, so I shot low and right)
https://pistol-forum.com/showthread....aining-journal
I post this because you might get some info out of skimming through it.
Ok here is the synopsis of what I found useful, in no particular order:
Regular effective dry practice. Note, this does not mean squeezing off clicks randomly at the TV. It means regular (daily), dedicated (in a safe direction), effective (EXACTLY as you would grip when firing) dry practice. 40 dry press wall drills should leave you smoked. If your shoulders and back aren't very tired after 40 dry presses, you are not getting as much as you can out of your dry practice.
Coin on the Slide Early on, I used the nickel / penny / dime balanced on the slide trick. I don't find this useful anymore, but you might. Balance a coin on the slide near the front sight. Press the trigger back and make sure it doesn't fall off. Repeat.
Grip hard No, harder than that. No, still harder. You want to leave "M&P" imprints on your palms. Hint: regular dry practice will help you achieve a hard grip.
Grip properly High up with the strong hand, 45 degree finger down on the support hand, wrap support hand under, thumbs forward and LIGHT on the frame.
Snap Caps Snap caps during range time can be a help. Insert 5 or so snap caps randomly in a few magazines. Slowly shoot. Note reaction when you hear a click rather than a bang.
Press the trigger straight back without disturbing the front sights. Ah, you say, that's easy. Yes, but this pretty much the key to shooting groups POI = POA. Meaning: you need to be able to see the front sight. If you wear bifocals, obtain a pair of +1 diopter full lens safety glasses. Or wear a AAA Petzl headlamp to illuminate the front sight. Both of these allow you to actually you know, see, the front sight so you can tell if you are disturbing it.
As to the trigger, on the press, DON'T STOP or STAGE the trigger. Press it straight back. It is not so much how fast you press, but that you press it in one go. Some very highly skilled people (most of the guys here) can press straight back quickly, and be accurate. Me, not so much. But I can definitely press straight back fast enough to get decent groups.
Note: you may have to fiddle around with your backstraps to see what works best. Try the S M and L backstraps and make sure that the one on the pistol is the one that minimizes sight movement.
Same for amount of trigger finger. You want wherever you get the least movement. It might be the crease, it might be the distal phalange, or somewhere in between. Again, least movement.
So you can see why you need to see the front sight, really really see it. You will be looking at it a lot in these exercises, hence the +1 reading glasses, and the AAA headlamp.)
Establish a metric, and shoot it live fire. One common metric is 10 rounds, slow fire, scored out of 100 on a NRA B-8 target. (Hint: NRA B-8 pdf files are available here for downloading and printing.) Shoot this as a baseline, then every time you go to the range. It does not matter what you pick, so much as what you pick you are comfortable with, and that you shoot it consistently as a metric.
Start a training journal You might think, nah, no one will ever read it. Actually, I have some of the best shooters in the country comment and read my posts, and any benefit I've gotten out of my practice has been magnified by this helpful advice.
Again, hope this helps. I have been where you are. Pistol-Forum has helped me immensely in getting to know what is "good" in terms of shooting, and is why I paid folding money to be a site supporter.
Good luck!
Rich