Move the sights or is it me...

Some of that could very well be your sights, but some of that is also you. I would work only on reducing the group size for now. Then you can see where your true personal point of impact is. A small group will also be an indication that you are not doing anything wrong.

Use lots of targets and limit the groups to five shots each. You might see 4 shots in a small cluster with one flyer (an outlier). You can consider the main 4 shots as the group in that case. A five shot cluster is best of course. When you have small groups that are a consistant location relative to point of aim, then adjust the sights. Pay no attention to the error from point of aim until then.

The "wall drill" is a good way to practice dry fire. Aim at a blank wall, and pay attention to nothing but the alignment of the front and rear sights with each other. The front sight should not move within the rear sight notch when "firing".

During actual live fire, you should be able to have a mental picture of exactly what the sights looked at the instant the gun fired.

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I think it’s important to note that you are probably pressing the trigger with the “pad” of your finger. Move your finger on the trigger to where your first joint break is.

Also, start dry firing at home and when you are at the range put a random empty case in your magazine. It will help you identify flinching.

Lastly, blue print your shot cadence. What I mean by this is shooting at the range and working fundamentals is not a race, it’s a very deliberate approach to fixing your problem. Shooting should be intentional and, you should understand what is happening with every shot.

You can’t duplicate or make a habit of something until it’s blue printed. You cant get faster until you master all the steps…. My blue bring is as below:
1. Grip:is the firearm in my hands properly
2. Trigger finger; where is my trigger finger placed
3. Sights, “front sight-Target”. Accept you can not stop the front sight from moving. I’m looking throigh the rear sight to the front… rear sights gonna be blurry, front sights going to be clear, target is going to be blurry…. If I’m shooting a dot. It’s simple. Dot-target…. Just know as with the front sight, the dot will not stop moving.
4. First sight picture, best sight picture,

Those first four are kind of happening all together but be connected to iAll above yes…
5. Deep breath
6. Internal thought “let’s go”
7. Front sight/dot on target….Press-press-press-press…. Bang!

Mentally be in the moment, train yourself to understand you are not taking the shot unless you are 100% certain your hitting the bull or black.

I also highly recommend shooting 25 yards on a B8. This will really allow you to see the mistakes and how much improvement you need towork toward.

90+ on a B8 is what I would personally consider good shooting.

Hard to beat training for any aspect of marksmanship. Consider myself very, very fortunate to have been on AMU team. Been shooting since 7-8 years old and doing many things wrong. Training conditions ones to reflex habits in every aspect. Grip, locking wrist and elbow , trigger position and control, sight alignment, breathing and follow through. I know lots of target shooting actions does not apply to combat but automatically gripping the same way, sight alignment and trigger control sure apply.
A cheap at home drill is an expanded “ blank wall” drill. Tape a piece of heavy white cardboard to a wall at eye level. position yourself so muzzle of pistol is 1/4” from wall. In set sharp lead pencil , align sights on white cardboard, focus on sights, depress trigger( use joint of finger or just in front of joint). Once pistol “ fires”, cock hammer push pencil back to breech and aim at the dot from first try. You will easily see whats going on. Use chart above and focus on each aspect of “ firing”. BTW, this was a AMUTU training aid taught to us by an old Master Army shooter.