Is this acceptable?
I have a fixed sight carry handgun that shoots to the left about three inches, and low about one inch at 10 yards. It's not me, anyone that shoots it gets the same results.
Are you talking double action or single action?
Are you right-handed?
Is "anyone" else getting the same result right-handed?
What's your length of experience shooting revolvers, let alone small J-frame revolvers?
The light weight, small grip, short sight radius and shorter trigger reach & heavy trigger of the little snubs can prove more difficult even for revolvers shooters who normally do much of their practice using larger revolvers. The older narrow sights can make things even more difficult because some folks find them harder to see and hold properly aligned throughout the trigger press.
I agree with another poster's suggestion to try some "ball & dummy" drills, to see how much anticipatory flinching may be occurring.
Small DA/DAO snub revolvers can often seem to be "less tolerant" of shooter issues and influences than larger handguns.
In the hands of an experienced revolver shooter, the little 5-shot J's can often demonstrate surprising inherent and practical accuracy.
I own and use more than half a dozen J-frames. Being a long time revolver shooter, I like the little 5-shot snubs. I often use mine (mostly aluminum or scandium aluminum models) to "chase the hole" or make called hits on little wooden clothespins spaced around the target backboard, usually at 5-7yds, but farther on good days. I often use them to check my "basics" from 25-50yds, too.