Hi

I think that having your thumb resting against the back of the neck when you are fretting a chords causes an incredible amount of tension in the muscles at the base of the thumb.

If you watch Lisa's video called The Opposable Thumb you will see that she actually has her thumb positioned well above the top of the fret board (ideally your thumb should be able to reach over and mute the low E string), which is a position that allows the muscles in the forearm and hand to be relaxed. Here's a little experiment - fret a C chord and allow you thumb to mute on the Low E string... you should have no tension in your forearm or hand at all. Now keep the C chord fretted and slowly move your thumb down the neck towards the floor... feel your hand and arm muscles tightening?

Personally the only time that I would have the pad of my thumb resting on the back of the neck is when I am playing barre chords, which unfortunately is a biomechanical necessity. It's also worth noting that you need very little pressure to actually fret the chords (apart from the dreaded 1st fret barre chords). Also check that your guitar is stable and securely resting against your body when you are playing as there is nothing harder than having a death grip on the neck while trying to switch chords. Another thing that you can try if you hand is starting to get tired when playing barre chords is to play the chord staccato or unfretted in places to give your hand a rest.

Good luck!