“I feel full” sounds a little unnatural, but not impolite at all. “No, thanks. I’m full.” (Natural, polite refusal. Not something to “feel”)

As simon3142 says, it's informal but it isn't impolite. In fact, we often say that we're full in order to be POLITE. If you are a guest in someone's home and they offer you more food, it is very impolite to simply say "No, thanks" (or worse still, just "No"). But if you say something like this: "No, thanks. It was lovely, but I'm completely full. I couldn't eat another thing!", that turns your refusal into a polite and non-offensive response. By saying that you are full, you can refuse extra food without insulting your host or suggesting that you didn't enjoy the food.

It doesn't sound impolite to me although informal.

I assume you are referencing food. I wouldn't be impolite to say "I feel full" If you are being offered food. you can always say, "No thank you I feel full" or "No thank you I am full"