Every time someone would ask Gary Craig "Does EFT cure ____?" he would respond, "Try it and see." I think that applies in your case.
How is your critical nature a problem for you?
What are you critical about? Everything or just some things?
Are you mean or angry when you are critical? You could certainly tap on the meanness and anger.
Are you critical because people don't do things the way you are doing them? Are you a control freak? You've got some tappable issues there.
I have a friend who has perfect pitch. He complains all the time about out of tune music he hears. He's very critical and actually experiences pain when he hears poorly tuned pianos. His critical nature goes along with being abnormally and exceptionally perceptive. Is your critical nature because you perceive the world more keenly than the people you hang with? Or are you just crabby all the time?
You can certainly make some deep changes with EFT but I can't say for sure you will make those changes because I don't know the depth of the problem, assuming it even is a problem, or how good of a tapper you are.