If we are listing credentials I'm also an NRA Certified Pistol Instructor, as well as a USPSA Certified Range Officer, worked managing a gun range for a couple of years, taught individual and group classes and was a competitive shooter until a neck injury forced me to give up shooting altogether.
During that time I worked with all kinds of folks who wanted to get their conceal carry licenses, their CMP, folks who were new to competitive shooting (or new to shooting altogether), and/or just wanted to learn to be better shooters and I can tell you that dry-firing was the single most effective tool I had when it came to helping people with the problems you have identified.
There's no sense throwing bullets downrange if you have no clue what you are doing wrong. Whatever it is someone is doing wrong, they are only reinforcing those bad habits by not doing some research and figuring out what is going on. Good for you for realizing that what you are doing is not working and that it is not the gun that is the problem. (Believe me, you'd be surprised how many folks SWEAR it is the gun ... LOL)
1. Take a look at this chart: Group Analysis - Pistol
I know you say you don't have any group but actually your lack of a group is actually a group! (I know, I didn't get it the first time I heard it either but after a week of dry-firing I cleared up some problems and then the other problems became easier to diagnosis. I found this to be true of most people I worked with.)
2. I've got nearly every book written by competitive shooters for becoming a better shooter written over the last 30 years and the ONLY one I recommend to shooters who just want to be a MUCH better shot (but don't want the silliness of "be one with the bullet" that some competitive shooters think is necessary) is one of the most recent. (No, I don't work for Mr. Seeklander). It is "Your Competition Handgun Training Program" by Mike Seeklander. It is available on Amazon or his website here: Mike Seeklander's Website
3. Your "wobble" is most likely due to one of two things. Either you are gripping the gun too tightly in an attempt to control recoil or you have some generalized weakness in the muscles you are using when aiming and shooting. Dryfiring (10 minutes morning and evening to start) will help alleviate both of those problems. Other folks have addressed dryfiring techniques above pretty decently so I'll not repeat that other than to emphasize that SQUEEZING the trigger without tightening the other fingers on your hands and maintaining no movement of the sight is what you are needing to work on FIRST. Speed will come later.
4. Your sighting problem is a little more difficult to address without seeing you shoot but you should only be making minor adjustments with a gun that is accurately sighted in. But I can probably give you some things to try if you can give me some hints about what you are doing.
So, if you don't mind, can you answer these questions for me:
Do you shoot with one eye open (which one) or both eyes open?
Are you right or left-eye dominant?
Do you shoot right or left handed?
What kind of stance do you most naturally fall to when you shoot? (Not the stance you were taught. The one that you find yourself in after you've shot a magazine or two and no one else is looking.)
Do you know where your natural point of aim is? If not, do you know how to find it?
Do you keep a journal?
Uhmmmm ... there are probably some other things I want to ask too but can't think of them off the top of my head, which is pounding right now.
ETA: Don't give up ... There was NOT a worse shot on the planet than me. Add that to the fact that I really didn't want to learn now to shoot in the first place (I married a damned JBT and he insisted I learn how to shoot.
). It took him a couple of years for me to "catch the bug" (no, really ... it took that long) but once I saw an IPSC match I was hooked!
: I really miss it now.
That's something else you can do. Find an USPSA/IPSC match in your area and go watch. Don't pay attention to the guys who blaze through the stages. Watch the ROs and how they treat the new shooters. Watch the new shooters. If you like what you see (and you will) gather up your guns and ammo, and equipment and go back next month. Competition shooting is NOT a replacement for good tactical training but it WILL make you a better, more confident gun handler and a better, quicker, more accurate shot.