Welcome to the Forum -
A 5.56mm Chamber can safely fire both the military 5.56mm and the civilian .223
Your rifle will feature better accuracy with the 5.56 since that is what the chamber was specifically cut for.
In a civilian .223 chamber, the 5.56mm NATO CAN cause higher than average chamber pressures and COULD cause a problem.
In that .223 chamber the civilian .223 round will be much more accurate than the 5.56mm would be in the same chamber.
What twist rate is your barrel??
And now that I have answered your question: Where's my Range Report???