How hot is your CPU running at? I had this issue when playing Battlefield too, as well as a few other games with my Radeon R9 270X. I tried installing new GPU drivers, Motherboard drivers, and then tried using older drivers and none of it worked. I also noticed another issue with my PC which was that the CPU was getting up to 90-100C whilst gaming - waaaay too hot. This was because I was only running the stock cooler on my i7 4790K. To cool it down, I bought and installed a new cooler which keeps it at around 50C whilst gaming and as a result of the processor being cooler, the issue stopped completely. If you need to check your temps, install a program like SpeedFan.
Hope this helps.