bb, you're pretty humormous ... ocd over onions and garlic ...
For onions, I usually cut the onion in half and then peel the skins off. By cutting the onion in half you have the edge of the skin to grab onto and it pulls off easily for me. I also run the peeled onion and my knife under cold water before I start to chop/dice which helps the teary eyes affect. And then I wash the knife and my hands again when I'm done chopping.
For garlic, I take the clove (or however much you are going to use) and smash it under my knife. Lay the clove as flat as possible, put the knife flat side down on top of the garlic and hit the knife with your hand to smash the garlic. This will easily loosen the skin and you can completely remove the skin. Then I continue to chop/dice the garlic.