Mobile apps are used in a variety of health settings, from apps that help providers, to apps designed for patients, to health and fitness apps designed for the general public. These apps ask the user for, and then collect and leak a wealth of Personal Information (PI). We analyze the PI that apps collect via their user interface, whether the app or third-party code is processing this information, and finally where the data is sent or stored. Prior work on leak detection in Android has focused on detecting leaks of (hardware) device-identifying information, or policy violations; however no work has looked at processing and leaking of PI in the context of health apps. The first challenge we tackle is extracting the semantic information contained in app UIs to discern the extent, and nature, of personal information. The second challenge we tackle is disambiguating between first-party, legitimate leaks (e.g,. the app storing data in its database) and third-party, problematic leaks, e.g., processing this information by, or sending it to, advertisers and analytics. We conducted a study on 1,243 Android apps: 623 medical apps and 621 health&fitness apps. We categorize PI into 16 types, grouped in 3 main categories: identity, medical, anthropometric. We found that the typical app has one first-party leak and five third-party leaks, though 221 apps had 20 or more leaks. Next, we show that third-party leaks (e.g., advertisers, analytics) are 5x more frequent than first-party leaks. Then, we show that 71% of leaks are to local storage (i.e., the phone, where data could be accessed by unauthorized apps) whereas 29% of leaks are to the network (e.g., Cloud). Finally, medical apps have 20% more PI leaks than health&fitness apps, due to collecting additional medical PI.