Just reinforcing some of what has been already said... It could be target panic, but it sounds like a shock-induced anticipation (recoil/noise) flinch. So, I would recommend using ear plugs AND passive (non-electronic) muffs with the highest NNR (try for at least 29NNR) you can find (without interfering with your cheek weld). If it's shot anticipation, not target panic, mentally it's a similar fix; start SLOWLY squeezing the trigger and then move your focus towards only on floating/holding your crosshairs on target until the gun goes off. If it's anticipation, basically you have to get to the point where recoil and noise doesn't phase you, period... A good solid set of foundational fundamentals will greatly benefit you, as you shouldn't have to think about what you're doing to set yourself up every shot (I'm not saying to be lax or careless, but to the point of basics, safety can be a routine aspect too); to this point, many range sessions with a .22 CAN help, but unless it's proper practice it will be useless or just reinforcing failure. Once you decide to transition to a larger caliber, recoil management and full focus ONLY on proper fundamentals, is key. If that doesn't help, the next step would be searching for a "minimum requirement" caliber (less recoil/noise) that will still accomplish you goal. If none of this works, I would recommend seeking professional help... Like has been said, this will need to be addressed similarly to target panic!
Quality of practice, time, and focus are more important than just round count. At my peak, I was only shooting an average of 100 rounds per week (match weeks were higher of course), BUT it was 4 to 5 days per week. Those rounds were made to count! Load development, zeroing, verification, competition, etc...