So am I right in saying that, officially, the US isn't at war?
The United States is at War.
It seems we have abandoned the custom of "officially" declaring war since the Korean conflict was accepted as being a war. Note that there has never been a official end to that war, just a end to hostilities. I can assure you, if you ever visit the DMZ your sphincter tone will go up a notch.
Some other US armed conflicts the US has been involved in that were never officially declared as war by congress.
Korean War:*
Viet Nam War:
Cuba: Operation Zapata (no US personnel)
Grenada: Operation Urgent Freedom
Somalia: Operation Restore Hope*
Bosnia: Operation Deny Flight*
Iraq/Kuwait: Operation Desert shield/ Operation Desert Storm*
Iraq War: Operation Iraqi Freedom/Operation New Dawn*
Libya: Operation Odyssey Dawn *
The US is currently at war in Afghanistan
Operation Enduring Freedom*
High level targets being acquired and engaged by drones in Pakistan as well.
* astrick indicates UN sanctioned*
"You were not there for the beginning. You will not be there for the end. Your knowledge of what is going on can only be superficial and relative" William S. Burroughs