Which browser are you using? Firefox? Which driver you used before last week when you have no problems? Are you GPU an Sapphire?
Some people like me has Sapphire 390 causing browser black screen since beginning of the year. Only way some of us find to fix it was moving back to 15.12 driver or downclocking GPU memory from 1500 to 1250mhz in newer drivers for browsing or while doing 2D tasks. In heavy 3D load no problem happens.
The browsers black screen crashes are not too constant. Sometimes only crash after 24-72 hours other times after 3-4 hours.
All of my browser crashes stay with screen black for first 60-90 seconds then frozen desktop screen turns back with artifacts then need to hard reset because screen is frozen. some rare times it cause an TDR and PC turns back after few seconds but last friday after TDR and Windows comeback some horizontal lines stay in screen. Today it crashed to 60 seconds black screen then turned back with frozen horizontal white lines flickering.
If i wait the black screen turns frozen desktop screen and only turn shut off computer after it then the crash save a TDR dump file at C:\Windows\LiveKernelReports\WATCHDOG. If i hard reset before black screen change to stuck desktop screen then dump files are not saved. All black screen/TDR browsers related crashes create 0x0141 atikmpag.sys bugcode.
But i played lots of games since march when this browser crashes started and i got not a single crash in any game. Crysis 3, Forza 6, No Man's Sky, Battlefield 4, Witcher 3. Even Furmark runs fine but open Firefox+Youtube wait some hours and you got a black screen of death. It looks to happen when youtube is opened even with no video playing.
This guy Sapphire Nitro R9 390 memory clock fluctuations causing crashes (have to reboot) discovered the problem is related to 2D clock/voltage GPU since decreasing memory clock fix the crashes in newer drivers while browsing. Make a test and see if it work out for you. Rolling drivers back after a DDU uninstall or downclock GPU memory.