Is it appropriate  to wear short sleeves in public?
Why do you want to wear short sleeves?
I'm more comfortable in it and it looks good
I see no problem with wearing short sleeves. If that is what you are most comfortable in, then go for it.
I hate people who judge others without knowing them.
It's true that people judge others based on their clothes and it's wrong. Still you should not care what they think, wear what you're comfortable in.