In simple terms, my hack diagnosis is it's probably an owweee of the ligament that holds the quad and shin muscles together via the patella.Otherwise known as patello-femoral disorder, and other-other-wise known as chondromalacia patella.
The indicator of pain going downhill/downstairs / Pain with a bend and loaded knee points to this problem. The ligament is maybe a little raw , maybe tiny tears, and when you bear weight with the ligament stretched over the kneecap, it freaking hurts. I always felt the pain felt like a rusty nail underneath my kneecap. The likely explanation is that you stessed the ligament during your hike, maybe because your kneecap isn't tracking right, or maybe because of improper muscle conditioning, or a combo of both.
I had a pretty serious case of this in August - went out for a solo backpacking with a lot of vertical ups and downs and had a really heavy pack. The condition with my knees was always there (feel it on long mountain descents especially , but trekking poles help) but the backpacking trip exacerbated the problem.
Anyway, I'd suggest ice and rest the knee. Don't do stairs, and get to your doctor if it doesn't get better in a few weeks with rest. They might recommend doing some conditioning exercises to strengthen muscles, particularly the interior quad muscle. Vastus medialis I think it is. My doctor mentioned that isolation of the muscle rather than full leg press exercises are better due to the current knee injury, and recommended some of these exercises and/or a true physical therapy program. If it is a serious case they might have you wear a brace, too, called a 'cho-pat strap' which helps the knee track better while your muscles are learning to hold it in the right place.
I'm sure someone else here will add more or maybe a different theory, but your pain is a classic symptom of chondromalacia. Good news is that it's not ACL / MCL stuff and almost always fixable with a physical regimen versus surgery. At least that's what my doc said.
I was off my knee for about 4 weeks, in the sense of no brutally knee-bending activity, and all the while doing exercises. Then gradually worked back into things. A few weeks ago I did a test-run of it on one of my favorite hikes with a ton of steep (about 4 miles uphill) and the knee was pretty good. Also good news is that skiing isn't as rough on this kind of injury as hiking is.