When something's swollen, it's puffed up, rounded, and misshapen. If you've sprained your ankle, it's likely to be swollen and may look more like a grapefruit than the body part you know and love.
When something swells up, it's swollen, and that can be anything from knees and glands to pregnant bellies. You can also use swollen more poetically: you can describe someone with a big ego as having a swollen head. A stormy ocean with big, angry waves is a swollen sea. And a state with out-of-control spending has a swollen budget, inflated by special projects and other expenses that there’s not enough money to pay for.