Is there an app that sends weather alerts push notification to the iPhone? I have seen similar apps on Andriod but haven't seen one for the iPhone.
Yes... WeatherBug. I don't use it on my iPod but it works great on Android. Their product description page mentions the same functionality on iOS as on Android, i.e. National Weather Service (NWS) alerts.
On my Droid it pops up with a red triangle in the notification area when there's an alert.