If you are shooting bullets less than 158 gr. the gun will shoot low, and it can have an effect on windage also.
.38 revolvers of that period and earlier were regulated for 158 gr. lead round nose standard velocity ammunition. No +P, no LSWCHP, etc. Elevation is engineered into the gun and usually will be very close with the noted ammunition. They determined correct sight dimensions so guns would shoot right and made them all with the same dimensions.
Windage can be corrected if necessary, but it is done by bending the frame (really!) and it better be someone who understands how to do it or a lot of damage can be done. It is NOT done by striking the barrel with a babbitt bar as you see mentioned from time-to-time on this forum. And, yes, I do know how, and have done so many times. This is how it is done by the factory.
The windage could also be your grip or how you are "seeing" the sights. Try the right ammunition before trying to do anything. A fixed-sight revolver can only be regulated for one specific load, all others will shoot away from the sights.