So, given your sight picture--are you shooting from a bench, in a rest--with bags under the muzzle and / or under the butt?
Is your hand well-conditioned?
I have several j-frames--and particularly with the lightweights (360, M&P 340, formerly a 442)--the mere act of finishing a trigger stroke can bobble the shot if your hand is not conditioned--and, if shooting unsupported but typically two-handed, using a double-action stroke.
Unless the butt is also padded on the rest, I don't think you can draw any conclusions yet on your 637's inherent POA. Have you shot it a lot? Have you a lot of experience shooting (lightweight) j-frames? If not, and if your hand is not conditioned, then I would shoot it a lot more with one specific ammo (say a 38+P 158-gr.), and concentrate on DAO shooting at 7 yards until you are thoroughly familar with this particular gun.
OTOH, if you are beyond the relative-newcomer stage to j-frame lightweights and a knowledgeable shooter, you might want to give S&W a call and see what they would do for you, and if there is any cost involved.
In the meantime, a good basic drill is to shoot Old Fuff's quad fives--e..g, five yards, five (DAO) shots, a 5" group into a blank piece of (typing, or 8.5x11.0) paper, and (eventually) in under five seconds. That kind of drill will get you acclimated to the kind of SD shooting these pistols excel at and help break any 'marksmanship' habits you may subconsciously bring to your carry-gun shooting.
on edit: I haven't checked my POAs recently because I shoot using a CT laser grip--and am getting transitioned to point shooting out about ten yards now. But, others have complained about the POA being off on their Airweights, and I am not convinced S&W is building them as carefully as they once were--at least if the 442 I had was any example of Airweights.
Jim H.