I was working on a project with my arduino uno connected to my computer. While doing this I shorted out my board for less than 30 secs, the board appears to be fine but is it possible that my computer is hurt?
It is a slight possibility. Most (all?) USB controllers have automatic current limiting (500mA) and the AVR processor has a natural current limit (when reached damages the AVR processor). However, a few folks have reported smoking a motherboard doing what you have done.
A powered USB hub in the middle is a worthy investment.