First, everything John told you I agree with fully. Adjustments between shots will definitely slow you down. Dry-fire practice will help eliminate the issue. And your gun's grip may not be ideally sized and shaped for your hand.
Note: I'm not an instructor or a LEO, or a former military firearms instructor, so you can take the following with any number of grains of salt.
However, I fairly recently was doing in my own shooting what you're describing in your own, and I found these two videos by Rob Leatham extremely helpful in eliminating my issues with grip adjustments between shots and shooting faster. In case you're unfamiliar, Rob Leatham is a world champion competitive shooter.
This one deals with how to grip a handgun:
https://www.youtube.com/watch?v=xNNlb7QjfGI
And this one describes the three most important things a handgun shooter needs to be able to do to shoot faster with accuracy (ignore the subtitles in chinese):
https://www.youtube.com/watch?v=li0rGtXh23I&t=7s
Now I won't lie, it's not nearly as easy as he makes it look, but it made a huge difference in my ability to hold onto the gun so I didn't need to readjust my grip, control recoil, muzzle flip, etc. in a relatively short period of time.
Hope that helps.
P.S. I should also mention, that in case you're interested in more Rob Leatham videos, he's got about 50 of them on youtube. Many of them are instructional.