Can you believe swimming helped my cooking? One day I realized swim goggles do well keeping chlorinated water from my eyes, so they could do the same with onion fumes. Indeed, they do! Your nose will still feel some pain, but I no longer dread seeing 'chopped onions' on the ingredients list of a recipe.
Make sure you get the goggles with the 'gaskets' around the eye piece. The ones with the foam do not do well against water or fumes. The right fit should create a slight suction around your eyes. Check the internet, if you need help with this.
A decent pair should go for as little as $10.