The .223 Remington and the military 5.56x45mm NATO are close cousins. Rifles chambered for 5.56 NATO can safely fire both; rifles marked only .223 Remington should not be fed 5.56 pressure loads. Check your barrel marking.
Low recoil, flat trajectory and huge ammo availability make it the most versatile rifle cartridge in America. Many states set minimum caliber rules for deer, and some hunters consider .223 marginal for deer even where legal; choose a bullet designed for big game if you use it.
Always use only the ammunition marked on your firearm’s barrel or slide, and follow the manufacturer’s guidance.