Monitor memory usage in an iphone app?

Yes. In Xcode, open your project and choose Run > Run with Performance Tool > Allocations. This will start an application called Instruments, which can be used to analyze your app. In that specific case it will record all object allocations which gives you a good overview of your memory footprint. You can use this with both, the iOS Simulator and an actual device. You should prefer to analyze the app while running on an iOS device to get optimal results.

Instruments can do a lot more to help you optimize your apps, so you should give the Instruments User Guide a closer look.