Aloe vera is great for soothing skin, particularly burnt, irritated, or sunburnt skin. Having your own aloe plant is a great idea, because you can use the gel straight from the leaves.
Alternately, you can buy an aloe vera gel. A lot of aloe vera gels don't contain all that high a percentage of aloe vera, but Natural Instinct Aloe Vera Gel contains 98% aloe vera. It is $12 for 125ml. Sukin Aloe Vera Gel is also $12 for 125ml, but I prefer the Natural Instinct gel, because the Sukin one has alcohol in it, which can sting burnt skin.
I have recently been using the Natural Instinct Aloe Vera Gel as an eye makeup remover, and it works quite well. It does sting my eyes a bit, and I do have a bit of trouble with my contacts getting blurry and irritated, but usually rinsing them a bit more thorougly than I would have previously seems to help.