One suggestion:
For now, stop seeing Par 3's as scoring opportunities. We all do it - we get up and think "Man...if I can hit this one close, I can make birdie." As we're rolling in our putt for a triple, we think "So much for the birdie."
Step up to the par 3 thinking, "What's the safest way for me to achieve a par, or at worst a bogie?" That might mean hitting your tee shot towards the edge of the green and ending up in a collection area. However, that's better than being in the lake or bunker.
As you improve, you can start getting more aggressive, and of course there will be some par 3's where there's no detriment to "going for it." Incidentally, I've often heard pros remark they often have to take this same strategy. While the par 3 seems like it ought to be an easy birdie for them, they frequently blow up if they try. They often have to go into par 3's realizing it's a hole they have to play for par.