What PART of the piecing process are you stretching? Each of the charms put together or block sections to block sections or blocks to blocks?
I agree with a lot of the advice listed above -
making sure you're cutting on grain and not bias,
don't pull the fabric through,
square up each item before you sew it to another squared up item,
starch will help,
PRESS don't iron,
start with a leader fabric (see Bonnie Hunter's site) so you don't have to pull your good fabric through when you start (that could cause stretching).
I get better results using a regular piecing foot NOT A WALKING FOOT. In an effort to save time switching the feet out...I tried using a walking foot and was not happy at all with the stitches and the 'bad' movement of the fabric.
Quilting is a LOT Of practice...keep going!
Nan