Based on a google search, which I know is the best way to figure out what's wrong with you, I think I get intermittent "runner's knee." My knee feels wobbly and stiff (which sounds contradictory) when I run, and then there's a dull pain for the rest of the day, increased wobbliness, and a weird "texture" (?) when I unbend it. The next day it's fine again.
I do squats to try and strengthen my knees/legs, but that's about it other than walking and running.
I'm thinking about buying this knee compression sleeve. Do you think this would help? Even when it doesn't hurt, my knee has always been a little baby. I'm fairly certain (had them fitted) that my shoes aren't the issue.
https://www.amazon.com/gp/product/B019ZK0WR6/ref=oh_aui_detailpage_o04_s00?ie=UTF8&psc=1
I bought these knee sleeves about one month ago for weight-lifting/running/basketball. Works fantastic for me, never slides down. Over 6,500 reviews at 4.8 stars.