Welcome to Android Central! This may or may not work for the Xperia V, but it's worth a try. You can try to wipe the system cache partition, which won't erase any personal data or settings.
1. While the phone is turned off, press and hold the Volume Up and Volume Down buttons together. Then, while holding these, press and release the Power button (keep holding the volume buttons).
2. The phone should turn on and a menu will appear. Press the Volume down button to navigate to the Recovery option. Press the Volume Up to select (if that doesn't work, use the Power button to select).
3. A yellow triangle and an Android logo will appear. Press the Volume Down and Volume Up button together and a recovery menu should appear.
4. Use the Volume buttons to move to the wipe cache partition option and then press Power to select.
5. When complete, select reboot system now and press Power to select.
Again, this might not work.