I think most of your problem is your expectations, so it is mostly a mental issue. Also, there is a huge difference between a 3-foot and a 6-foot putt. Do you know most 10-14 handicap players only make 50% of their putts from 6 feet? And that pros only make 75%? We have a tendency to think they make them all, but they don't. So you need to go easier on yourself. You, on average, will only make 2 of the 4 6-foot putts you see each round. And if all 4 6-footers have considerable break, only making 1 of 4 is a reasonable outcome and therefore should be your expectation. Better than that is a bonus. What I am saying is you shouldn't lump a 5-6 foot putt in with the 3-footers. They are not "little putts." And manage your expectations in a realistic manner so it doesn't make things worse.
Yes, as you get closer to the cup those percentages should increase of course. But you should never think you should make them all or it will be self-defeating. We know even the pros miss 3-footers. ALLOW ourself to miss 1 or 2 3-footers per round. Then, my guess is you will limit yourself to that and won't be missing 3-4 real short ones per round and "driving yourself crazy."
Yes, as you get closer to the cup those percentages should increase of course. But you should never think you should make them all or it will be self-defeating. We know even the pros miss 3-footers. ALLOW ourself to miss 1 or 2 3-footers per round. Then, my guess is you will limit yourself to that and won't be missing 3-4 real short ones per round and "driving yourself crazy."