Whenever I absorb a dragon soul or when I learn a new shout from approaching a word wall, I hear the whistling of wind but then... its just silent.
I can't remember since when it started happening, first few times I ignored it but now I miss it.

Maybe my sound file got corrupt or something?
All the other sounds seem to be working just fine, including dialog with NPCs.

Try verifying your files.

what do you mean by "verifying"?

I believe he means that you should go into your steam library, right click on Skyrim. Choose Properties -> Local Files -> Verify Steam Integrity of Game Cache...
Correct me if I'm mistaken.

I had a similar problem. Verifying on Steam fixed it. (Also fixed some dialogue issues)