All the facts and figures he was reciting were starting to make my 'head swim'. [=starting to make me feel confused, unable to think clearly, etc.]
The schools competed in a 'swim meet'. [=a swimming competition with many races]
When he gets 'into the swim of things', he'll be much happier.
(..) yards beyond the end of the bridge. Behind the troopers were dozens of possemen, of them on horses, and perhaps white spectators. Can you swim? Not many swimming pools for black folk where I come from. Yeah. Andy. It's Bayard. Everybody there? Yes. (..)2014 Selma
(..) Yeah, but the biggest thing is getting your hair wet up. I got my hair pressed that same morning and it was wasted as soon as I hit the water. I should have worn a swim cap like Mama said. See, I asked my mama could she make my hair like Coretta Scott King had hers at the Washington March. (..)2014 Selma