Hi. I learned my first word of power in Bleak Falls Barrow and absorbed my first dragon soul near the watchtower near Riverwood. Until then everytyibg was fine. Then I learned "Fire" in Dustman's Cairne. Since learning it, I killed two dragons but the word still isn't active. Am I doing something wrong or there is a bug? Please help me, cause it's pretty annoying!
That depends on what you're doing. You have to activate it manually by going into the spell screen, highlighting the Dragon Shout, and pressing the appropriate button ("R" for PC users). If you're doing that, and the shout still isn't being marked as active, then you have a rather serious bug.