You need to adjust the amount of tension you are using when applying pressure with your fretting hand. And you may need to learn how to relax your hand when you are not using it.

Heres an exercise you can do that will tell you if you are pressing to hard.

1. Rest your finger on the string lightly so that it is muted while constantly strumming.
2. Slowly apply pressure until you hear the string ring out clearly.
3. Dont apply any more pressure than that.

That is all the pressure you need to apply to make that string ring, you will notice that it doesnt require that much.

Also pay attention to your hand tension when you dont actually need to use it, the more you relax when needed, the easier it will be to play and the less stress on your hands it will require.