5.56 military ammo fits military chambers that are typically larger than .223 chambers. So, theoretically you could end up jamming a hot loaded military round in to the rifling of a .223 chamber which would significantly increase pressures.

Discussions of this have occurred in the past on Joustericon and I don't think anybody came up with an example of that happening. But rather than guess, just take a magic marker to the bullet of one of your cartridges, chamber the round (preferrable not indoors), remove the round and see if there are any marks on the bullet. That will tell you if it's touching the rifling.