A young child has very few things that make them feel safe and secure and in control. Parents are definatley #1 but I believe sucking is a very close second. Babies suck to make themselves feel calm and happy, why would you want to take that away from your baby?
There are a lot of different books and dentist that will say thumb sucking is bad for a babies teeth, But who cares! if it makes your little baby feel happy and safe let him do it. Instead of trying to figure out how to stop him from what is a natural comforting tool in childhood, put your time to figuring out how to pay for the braces in 10 years.
My first one sucked her thumb while in the womb. I have a very clear untrasound picture of her doing it...it is so cute! She grew out of it eventually and yes her teeth coming in did take a toll on the skin. I had to take her to the doctor once because she broke open the skin and it got infected. Some topical ointment for a couple of days and she was fine and sucking the thumb again.
My second daughter is not a thumd sucker but instead she sucks on her arm. I know it sounds weird but it is the cutiest thing ever. She pushes up her sleeve at night and puts her arm up to her mouth and sucks on her wrist where a watch would go and she falls asleep.
The reason your baby is doing it when he is tired or annoyed is because he is comforted by it.
As a new mom the advice I would give to you is....don't worry about the little things.
Good luck