I almost passed out after cutting my finger even though I hardly lost any blood, is this normal?

I've never had a problem with blood before, my own, or anyone else's, but after cutting my finger today I had a strong physical reaction: I felt dizzy, like I was going to pass out, had trouble breathing, and could barely hear for about a minute (I heard a ringing and it felt like I was wearing ear plugs)... the pain wasn't intolerable, and I didn't lose a lot of blood, so what happened??