Most handguns are set for a point-of-aim shot, not a 6 o'clock hold, and they are usually sighted in for about 25 yards. If you are shooting at 25', the bullet is still on its way up to the point of the trajectory the sights are set for, and therefore hits low. The same thing would happen with a 9mm or some other caliber that has a higher velocity, but you wouldn't notice it as much because faster bullets mean longer, flatter trajectories. The .45 has a slow bullet and a looping trajectory, so the difference is more notable. If you ever take a 50 yard shot, you will probably notice your shots dropping in about 6 to 8 inches below your point of aim, as they have passed the midpoint of the trajectory and are on their way down.
Your problem with flinching and dragging the muzzle down is the bane of handgun shooters: recoil sensitivity. In training, I've found most shooters respond well to the old ball-and-dummy drills. This works easier with a revolver, but can be done with an auto if you have some commercially available dummy rounds or a buddy to help you. To do the drill, you load several mags from a pocket containing live rounds and dummies without looking, so you never know if you are getting a dummy or a live round. When shooting, sometimes you get a shot, sometimes a click. If flinching is your problem, when you get a click you will drag the muzzle down. As you continue, you will gradually stop flinching. Another way to do the drill is to have a buddy load for you, out of your sight. Sometimes he loads a round, sometimes not. When he hands you the gun, you fire and you get the same effect. This way is a bit time intensive, but you don't need to buy dummy rounds.
Starting handguns with a .45 is a little tough. Good luck.