LM2576-ADJ bipolar power supply troubleshooting
What might be a showstopper is that your input supply voltage is only 12.86 volts and that is insufficient for this regulator if it's producing 12 volts on the positive output. You'll probably need another volt of headroom for this to work correctly. It's not an LDO switching regulator - the data sheet is probably a little cautious about this but it does suggest that 15 volts is the minimum.
Ignoring any other potential circuit faults, the layout is not-so-good in that you will have problems with noise and regulation when you solve the circuit issue. I will also mention that I can see that you have fixed the negative voltage regulator error shown in the data sheet - the ADJ pin does need to be set with a potential divider for that circuit to work and you have correctly done that it appears. Anyway, these are my layout recommendations: -

Keep the ground plane exclusive to one layer (underneath usually) and route connections only on the top copper where possible.
Where connections cannot be exclusively routed on the top copper, make a bypass connection on the underside but, keep it as short as possible so as not to disrupt the ground plane.
Use thicker connections for power feeds to the chips, inductors and decoupling capacitors.
Keep switching tracks as short as possible
Use component reference designators in the silk screen
Get the inductors much closer to the chips - at the moment those connections will form loop antennas (especially as the grounding method you currently use is poor).