How exactly does a dragon soul work? I have killed oh about 10 or so dragons (level 27) and get dragon souls, yet I can only use "2" of my shouts that "require" dragon souls? I got the second one after I went to the greybeards and gained the whirlwind shout. Is there something I'm missing here?

ya go searching for new shouts and you use the souls to unlock them

If you explore you'll see a dragon looking symbol on the map. Go to it and you'll see and dragon and you'll see a word wall. You will then learn the word and then go into magic then shouts and unlock it with dragon soul. Eventually you'll start getting all the words for a shout and you have the choice to unlock them if you like them, I think it's for making them more powerful. Also there are word walls in dungeons that are marked with trident looking symbol. My advice is find the dragon symbols to get you started if you don't want to progress into the story too much.

This sounds to me like you already know the shouts, but haven't unlocked them (as opposed to the previous answers which are interpreting your question as meaning that you haven't found any other shouts). If you highlight one of the locked shouts, then look in the bottom left of the screen, you'll see that the list of options includes "[R] Unlock" - just press R to spend a soul and unlock the next word of a shout.