I would add "的" between "一个小时" and “泳”。
So the full sentence is “我游了一个小时的泳”.
Because "一个小时" is a attributive, which is used to limit or explain nouns after it. You swim for 一个小时, not for 两个小时 or whatever. "的" is similar to 's in English, for example, one hour's swimming, two hour's drive.
So it sounds more natural when you say “一个小时的泳”.