I would not mess with the DPI of your mouse. If you are going to mess with sensitivity, do it in game. Leave your other settings static, and mess only in game, unless you just have to turn down windows sens.
For the most part, I doubt its your accuracy, and more your nerves and trying to go too fast. I'm a pretty good FPS player; I'm also pretty accurate clicking on everything, EXCEPT sometimes when I'm trying to kite as an ADC. I'm a good enough FPS player to know that my accuracy isn't as bad as it is when I'm misclicking slow ass champions in league, esp. when I never misclick tiny minions. The problem is nerves. I've almost gotten over mine, but not quite.
Also, its going too fast. You are spamming your cursor back and forth as fast as you can, when that is not necessary, esp. early on before you have a lot of attack speed, and is just going to hurt your accuracy. Also, you are probably over-exaggerating the distance between the clicks, which again hurts accuracy.
I used to do what you do, I would be kiting, or fighting, and click right beside the champ, and run into him, basically suiciding or completely screwing myself. Most of this was nerves. But, something I did, and you can do, is start using attack move. This will make sure that when you misclick, you at least attack something instead of running into the pile and dying. You might miss some kills from time to time, because you hit a minion instead, but its better than giving up your position and dying, IMO. You can eventually weave regular clicks back in, since those are more responsive, IMO, but using attack move will help you maintain your positioning, which is more important.
The reason I say attack move is less responsive, is because it is taking both hands to achieve the same result as one. I actually misclick slightly more using attack move, but its not as detrimental as a single misclick with the right mouse button. I sometimes overshoot or undershoot the target because I click the attack move button before or after the mouse reaches its target, but again, this is an acceptable outcome compared to misclicking beside someone and running to him with right click.
I actually rebound attack move to my space bar. I'm so used to using spacebar while doing everything under the sun, because of FPS games and WoW arena, that its an easy button to spam while doing things and It feels natural from years and years and years of using it while WASDing. But, put the button where you feel comfortable.
But if you dont want to use it, and still want to use primarily right click, just slow down. Take your time clicking on people, you dont have to spam your movements as fast as you think you do. An easy way to get used to this, is watch your attack animation. Watch the actual projectile leave your guy. When it leaves, then you can move.