What's your question really, since you already posted the schematics for both regulators?
What you need is two galvanically isolated voltages (like transformer with two secondary windings) or a transformer with center tap to supply the circuits you have posted.
Why bother with 317/337 since you could use 7815/7915 (no need for resistors)?
Your circuit looks all right ..
All what you need is a transformer with CT (centre tap) or 2 secondary windings and recifier bridge(s) ..
With these regulators to achieve +/-15V output you need input unregulated voltage of +/-18 (under full load) or higher .. If you don't want to generate to much heat you can reduce the input voltage from +/-30V to, say, +/-20V ..
Regards,
IanP