"Swirling" can mean to go around and around. I think of SWIRLING LEAVES caught in a small whirlwind or SWIRLING WHIRLPOOLS below a bridge crossing over water.
In "Starry Night," the painting reminds me of looking at whirlpools in the ocean, except you're looking up into this incredible sky, so full of motion.
By the way, who is the artist for your profile picture? Is it a character from a video game?