"The cat who got the cream" is a sort of idiom or expression. To feel like "the cat who got the cream" means to feel good. To me "the cat who got the cream" suggests a cat that STOLE some cream that she wasn't supposed to get, so it means to feel good, perhaps in a mischievous way. The writer is making a half-joke, a pleasantry, because of a parallel between a real-world situation and the expression. A similar expression to say that somebody was "smiling like the cat who ate the canary." That definitely means a _mischievous_ grin.

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To feel like "that cat that got the cream" means to feel very satisfied with yourself... like a cat that literally got some cream to lap up. In the writer's situation, there is literally no cream.