What should I do if I think my best friend is gay?
Would it upset you if your best friend was gay?
No, but it's a good friend who might have betrayed my trust.
It's understandable that you may feel uncertain about your friends sexuality. Acknowledging the questions that you have and how you feel about your friend is good. It will help to prevent you from acting different towards your friend.
What if he's just shy.
It's possible that he's just shy, but you should also think about how you'll feel if your suspicions are true. You don't want to overreact and say something inappropriate just because you're shocked. He should know that you care about him no matter what.