Currently my character cannot learn additional Dragon Shouts beyond Whirlwind, Unrelenting Force, and Kyne's Peace. According to Bethseda, they are working on a fix to the problem, but in the chance that a fix is impossible, would it be possible for me to get through the game with just the 3 shouts I have listed. Thanks for any input.

No you need a few quests for the main story

Why is this in the Mods section?

What problem is it they are working to fix? Is it that you have gained the words, and also have dragon souls and it is not working for you? I have not heard about this problem. If you could provide more info, maybe some folks could help you. What words do you have that you have not activated? How many souls do you have? Is pressing R not working?

Maybe its just a touch of Laryngitis.

Unless you got Dragonrend, Alduin will "fly" all over you.