I recently caught an Aron with red eyes. If I evolve it, does it lose its special eyes? Do the eyes have a function or is it just for looks?
You've caught a Shiny Pokemon!
Previously officially known as alternate coloration or rare coloration... [a Shiny Pokemon] is a specific Pokémon with different coloration to what is usual for its species. It is one of the many differences that a Pokémon can have within its species.
They are generally quite rare, and the game will warn you if you try to transfer them.
Should I evolve it or not? Will it lose its special eyes?
Shiny Pokemon will remain shiny after evolution, though it's worth noting that Lairon and Aggron have slightly different Shiny colourations. The eyes will remain red, but also you'll notice a more steel-blue rather than charcoal/dark grey underbelly.
Will it help in any way or is it just kinda for looks?
Just for looks, and bragging rights. Shiny Pokemon aren't any better or worse than their non-shiny counterparts, stat-wise.
You can read more about Shiny Pokemon on the Pokemon Go Wiki
Here are some pictures for comparison. Regular Aron & evolutions:
Image from Forbes.com
And the shiny variants: