If you want to track heart health, here are a list of apps I tried during my experience with an elevated heart rate. The list is not exhaustive, but if you want to track sleep and heart health, these apps will get you going.
HeartWatch. This one kicked off the alerts that made me realize something was wrong. The user interface is complicated, but I think this app is the one to beat if you care about data from the Apple Watch.
AutoSleep. Part of the HeartWatch family, it knows when you get to bed, so you do not have to set it on the iPhone manually. The data integrates with HeartWatch.
Sleep Cycle. A mature, full-featured app for tracking sleep on the iPhone. Perhaps the best of its type on iOS.
Sleep++. A decent app for tracking sleep with the Apple Watch. I found it to have bugs that interfered with using it. It's popular but not one I can strongly recommend.
Heart Graph. As the name suggests, this app graphs your workouts in heart rate zones and makes comparisons across workouts. It's a basic app but does the job.
Motifit. Another workout tracking app, but this one displays a real-time heart rate on the phone. It only displays the large real-time rate when you start a workout, however.