spin [intransitive, transitive] to turn round and round quickly; to make something do this
(+ adv./prep.) The plane was spinning out of control.
a spinning ice skater
My head is spinning (= I feel as if my head is going round and I can't balance).
spin round/around The dancers spun round and round.
spin something (round/around) to spin a ball/coin/wheel
We placed our bets and the croupier spun the roulette wheel.
swing [intransitive, transitive] to move backwards or forwards or from side to side while hanging from a fixed point; to make something do this
His arms swung as he walked.
As he pushed her, she swung higher and higher (= while sitting on a swing).
swing from something A set of keys swung from her belt.
swing something He sat on the stool, swinging his legs.
Some women in developing countries often "spin or swing their hair around" after washing it to dry it off as shown in the picture.
I am not sure if we say "she is spinning or swinging her hair around".
Also, I am not sure if people say "swing something around" because the "swing" movement doesn't go around but randomly back and forward or side to side.