There are various methods of fretting, and I don't want to stir up a hornet's nest or start a lengthy debate, so what I'll start with is this: see if you can watch a channel like Paladium or something, maybe just browse YouTube and check out players that play the kind of style you're after, but make sure you're watching videos of them playing live. For rock, so guys like Slash, Neil Schon, etc, you will notice that most of the time they wrap the thumb of their fretting hand around the fretboard, forming a more natural "grip" position with their hand rather than the more traditional, classical position of having their thumb pressed directly behind the fretboard at all times. They will move their thumb behind the fretboard when they need to in order to fret chords properly, then then move it right back, especially when playing lead.
What I think this technique does is allow them to keep their wrist relatively straight. Regardless, even though they may look like they are "gripping" the fretboard, I guarantee you they actually have a very light, relaxed touch.
Try to keep your wrist straight when you can, and make sure you're not death choking the fretboard. Try different positions with your thumb, allowing it to wrap around the fretboard so that the neck sits more in your palm, and see if that helps (while it might, it may be difficult or near impossible at first to fret some chords like that... but give it a chance and see how it works for you). Tension is not your friend, and pain is a red light telling you to stop. If you feel wrist pain as you play, stop. If your wrist is sore after playing, you need to stop for as many days as it takes so that it no longer hurts. If you push it, it will get a lot worse fast.
Let us know how you make out, as I'm sure other people would be interested in what works for you and what doesn't.