You'll be fine. The "hot side aeration" stuff you read about is one of those things that is hotly debated, especially as to if it has any effect on the homebrew level.
When using my wort chiller I slosh it up and down as well as stir the hell out of my kettle to move the beer across the coils, to get the wort cool faster, and start aerating the wort prior to yeast pitcihing, and I've never had an issue.
A lot of those "boogeymen" you read about in How to Brew, like autolysis, and has, are really worst case scenarios that rarely happen to homebrewers despite the boneheaded things we do to beer.
Read this thread What are some of the mistakes you made...where your beer still turned out great!
And you'll see.