While I can't offer any true medical advice, I did that this problem a few weeks ago. I basically avoided doing any heavy pressing for a week or two and did a lot of stretching for my wrists and forearms. I slowly worked my way back into pressing and not it doesn't hurt nearly as bad as it did, though if I do too much volume at a heavy weight it will start to hurt again slightly. Some people say fat grips and fat bars help because it disperses that pressure over a larger area in your palm, so you might give that a shot after at least a good week of solid rest. A solid pair of tight wrists wraps when pressing help a ton as well.
Like I said, no true medical advice, but that is my experience with that issue. Take it for what it's worth.