You can check the device console to see if the app is "crashing" due to an expired / invalid provisioning profile. For information around seeing that information in the console, you can get that information here.
If you want to build in provisioning profile checking into your app to see when the app provisioning profile is set to expire within the app itself (or the certificate used to sign the app), you can see that here. Accessing the profile information at runtime is challenging, but can be done.
However, if you just want to confirm that the app is crashing at launch due to the profile, simply check the device console.
Also, free account provisioning profiles will last only 7 days. So you have a week to run the app. But if you build the app when you provisioning profile is 3 days old, that only gives you 4 days from when you build the app to a device.
Also, the having a new provisioning profile in Xcode has no effect on the device. When you run on the device from Xcode (or install an .ipa from a web link), iOS installed the profile on the device. If you don't run from Xcode, your devices provisioning profile will be older than the one in Xcode and the app will not run.