The expression is correct, however "I am" is being emphasized so, in cases like this, we tend not to use a contraction (use "I am" instead of "I'm")

You'll see how good I am at playing football!

Sure. That will work. "Good" in this case is modifying (adding something to) "I am." So you could also say, "You'll see how well I play," in which you are now modifying your playing. If I were talking to friends or someone equal to me, I'd use the first sentence. But if, say, I were applying for a college and a scholarship, I would use the second sentence; it's more formal and in sticking with the formality of, say, getting into a college or something like that. Hope that helps.