I have a pile of shout words that aren't activiated and I've killed at least 7 dragons by now, but my character isn't able to shout these new words. What gives?

Selphie

Have you highlighted the shouts in your magic menu and pressed the X button?

Go to your shouts and press X to unlock the ones that you have but can't use

Ok, killing dragons doesn't teach you the words, they give you dragon souls which are needed to activate the ones you HAVE learned. To activate them, go to Magic>Shouts. Here will be your list of all the shouts you've learned. The darkened ones are the ones you haven't yet unlocked. To do so, simply press 'X' on the shout (provided you have a dragon soul).

And there you go!