I got worse and worse as time went on.
I like to end each range session with a "ball and dummy" drill. I mix up some live ammo and two action-proving dummies, load the mag with my eyes closed (good practice!), insert the mag, rack, and shoot.
When a dummy round comes up, I should see the hammer fall and the gun remain still.* If it jerks on the dummy round, I jerked it: a flinch. Now I've got some real concentration to do.
Also, at speed, folks tend to accept a less precise sight picture than for precision, and that's fine. But don't fall into a shooting rhythm where you're firing according to when the sights
should be back on target, instead of when they actually are.
And some folks try to shoot faster by jerking the trigger suddenly when the sights line up. You can find that and work on that just the same as a flinch.
My bet is flinch. Tends to come on (for me) at the end of the session, when I'm tired. Shaking without flinch doesn't tend to put me off target.
*BTW, now you get to execute a tap-rack-reacquire drill. More good practice!
My hand and gun were shaking so bad
Sounds like you're over-gripping the gun (which many say isn't possible!
), so you're wearing yourself out too fast. Or maybe an awkward stance (isoceles is not for everyone), or training too long; lots of possibilities.
Could be, also, that .45 isn't your caliber. It isn't everyone's.
Getting a trainer to look you over (a pistol shooting trainer, not simply a "the required CCW course" trainer) could answer your questions best.