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.
(..) Beat that. Come on, Nemo. How far can you go? - My dad says it's not safe. - Nemo, no! Dad? - You were about to swim into open water. - No! Good thing l was here. - He wasn't going to go. - He was too afraid. - No, l wasn't. - This does not concern you. You're lucky l don't tell your parents. You can't swim well. - l can swim fine, Dad, okay? - No. lt's not okay. You shouldn't be near here. You'll start school in a year or two. No. Just because (..)2003 Finding Nemo
(..) l can't. l'm involved now. You let go and l'm gonna have to jump in there after you. Don't be absurd. You'll be killed. - l'm a good swimmer. - The fall alone would kill you. lt would hurt. l'm not saying it wouldn't. But l'm more concerned about that water being so cold. How cold ? Freezing. (..)1997 Titanic
(..) Sir, you need to go. Now. Security, sweep the area. Great, we're dead. We're dead. That's it. I'm dead. You're dead. Everybody's dead. - Can you swim? - What? Can I swim? Yes, I can swim. Why? Carrots! Hopps! Judy! We gotta tell Bogo! Wow, you are one hot dancer, Chief Bogo. (..)2016 Zootopia