Animal/bird screen, and I don't leave home without it.
There are a couple here that rail against it..probably more prone to clog on their BKs.
If you can't climb up there right now, go out in the yard with a pair of binoculars, you should be able to see how bad it is.
Thinking more about your weak draft, I'd say chances are pretty good that it may have been a back-puff; Box filled with wood smoke and some creo smoke burning off the box, then it ignited and pushed acrid smoke out of the stove. I agree with bholler, get that chimney section up there. Once the leaves come in you'll barely be able to see the missile silo strapped to your house.