This is actually the 2nd time I encountered this bug. When the opponent (Priest) plays Psychic Scream and ended the turn, on my turn I am not able to draw any cards from my deck, and when it returns to my turn again after the opponent ended his/her turn, I am not able to play any card.
Below is the video that I captured, hope it helps:
The Psychic Scream issue is well known and affects all (?) effects which shuffle cards in opponent’s deck. See:
If you encounter again an issue which prevents you from playing, you can force-quit Hearthstone (Alt+F4 in Windows) and restart it right away to return to the game in progress. This workaround should clear the invisible cards from effects like Psychic Scream (though future draws might still have the same problem), until a proper fix is implemented by Blizzard.
Thank you for sharing the status update from Blizzard and the force-quit and restart method, will try it out if it happens again. Hopefully they get it fixed soon.