See if some games are running fine then this may well be the case of GPU drivers and the game settings.
Try disabling Anti aliasing and Shadows and see if the problem persists.
Also, try getting the latest drivers for RX 480 from the link below:
http://support.amd.com/en-us/download
Completely uninstall the existing drivers and do a fresh install of the 16.7.1 drivers. Check if the problems are gone.
If not, RMA (return to your vendor for replacement) your card ASAP, if it is still under warranty.