If I have regular 5.56mm ammo and I buy 5.56mm armor piercing ammo does the armor piercing ammo just add to the regular ammo, or can I choose which one I want to use? I think it is stupid to just clump the two armor types together so you don't know which one you are using.

Magic key aka "2".

Or 'up' on the D-Pad for Xbox and PS3.

2 ways. Like people said, the top middle option of the hotkey menu is always defaulted to ammo swap (#2 on PC keyboards and up on console d-pads).

The other is to actually go tot he ammo section of the inventory screen. All ammo types not for your gun are greyed out. Pick one that is for your gun and "use" it to equip in current weapon just like you would to equip a weapon or apparel.