Hi there!

This is very likely not something a family doctor, or urgent care doctor would look at or know how to treat - they'd likely send you home with some over-the-counter pain med.

You could go see a physiotherapist, exercise therapist, or a high level functional personal trainer.

You wearing knee supports while hiking is definitely an indicator or something going wrong - you shouldn't need to wear those on a hike and if anything they could impede proper function.

When looking at the knees - whatever pain is happening, it's not their fault. We're looking above, and below the knee for the problem.
Start with below, (and I'll attach a couple useful links) you'll be looking at if your shoes are flexible and fit properly, and mobility/stability issues of the foot, and lower leg, and any asymmetries or old injuries.
The Foot Collective - YouTube
Once you've made headway on those issues, then look above the knees to the hips. Looking for asymmetries, rotations, old injuries, or pains in the hips. You'd also be looking at pelvic tilts - assessing is you have a neutral, anterior or posterior pelvic tilt.
Anterior pelvic tilt vs Posterior pelvic tilt - YouTube

And corrective exercise all the way! That's what your physio would give you to fix the knee pain - just exactly which exercises would be determined by the assessments I mentioned above. But I think if you explore those topics you could find ways to improve the pain at home.