Before i go to see the doctor... I have something growing on one of my tonsils. Tonsil itself its larger than the other one, on the other side, and it is pretty oddly shaped as well. I first noticed it couple months ago i guess or maybe a year ( or even more, not sure ) but i did not think of it at all. I believe its not any bigger than it was year ago.
I found something similar to this on my tonsil too. I just got back from the doctors to find out that mines a tonsil stone. This means it should go in a few days and requires nothing but paracetamal. However, I only found mine a few days ago so I'm not sure if you have the same thing as it's been there for so long. As your post was two years ago I guess you've got it sorted but I hope this is helpful for anyone else who has something similar