Godel's results are for the 1st order variant of the Dedekind/Peano theory of the natural numbers. Consequently, there is no contradiction with the inferential completeness (every proposition is provable or disprovable) or self-provability of formal consistency in the higher order theory.
Also, Godel's proposition "I'mUnprovable" does not exist in the higher order theory because it doesn't type check.