How do I restart my phone without using my power button?
There are two possibilities: 

Reboot via ADB


Enable Developer options on your device and enable Android Debug Bridge (ADB). 
Install the Android SDK or at least the minimal ADB environment on your PC.
Now connect your phone via USB to your computer
Execute adb reboot


Reboot via app (requires root)

Rebooting your phone from within an app requires root permission. If your device is already rooted you can use one of the reboot apps from PlayStore: