Thanksgiving Riddle

Ben learned this darling song/riddle at school.

I am not a drumstick, no not yet.
I need to eat more, so fat I get.
Corn is what I like, and lots of grain.
Sometimes I gobble. Can you guess my name?

[Hint: You're supposed to answer "Turkey!"]

I see you've guessed my name on your first try.
I have a problem and you know why.
Could you be so kind? I have one wish.
Help me out, and EAT SOME FISH!!!!

(The tune is very similar to "I'm a little Tea Pot")