It does sound a lot like you need about a handspan more in the back across the shoulders. Giving the shirt a waist as Rob suggests (one way or another, for there are a couple-three) is a good help.
Search this site on "triangular expansion arrays" for putting that ease into your back -- at about shoulder blade level, from trapezius muscles extending to about the bottom of the shoulder blades. A bit farther than that, say as much as four fingers' worth, is okay too.
A hauberk proper is a large and knee-length coat of mail. Yours sounds technically more of a haburgeon -- a later, weight saving development. One well suited to infantry/archer type armor. Are you doing a historical period, a fantasy, or some Tolkienish blend of both?
You'll need to taper it into the waist, so that you don't have as much excess material to deal with. Search for "chainmail contractions and expansions", and you'll see what you need. That should help some, even though you're using a t-shirt style. You also want to expand across the back of the shoulders so that it doesn't pull when you reach forward. That should free up movement rather well.
I am working on a mail hauberk for use in mounted archery. It's 3/4 of the way finished, and I'm trying to make it fit better.
At the moment, it seems to bind up when I reach across myself (like I would when drawing a bow). More importantly, it's done in the T-shirt style. But while it fits in the shoulders, when I belt it at the waist it's too large, and results in some large, uncomfortable folds.
This is the first hauberk I've made, and I have no idea what to do to make it fit better.
If anyone has any advice, I can take pictures of it to make things clearer.