What should I do about an overflowing septic system?
It is entirely possible that if the toilet was running hard enough that that is the source of the problem.  Assuming the weather conditions are fairly dry and surrounding ground is not saturated, I'd give it a day or two to subside and let the leach field catch up. If the problem doesn't clear quickly with the toilet fixed, I'd call for a pump and have them check the backflow of the leach field to determine if there is blockage downstream from the tank.  Good luck.