Sore Quads while running

Guessing there are micro-tears in the muscle which haven't healed. I would recommend massage--quads are big muscles and pretty amenable to that. You can try foam-rolling, but if you can find a massage therapist who knows their stuff, that will work wonders. Easy swimming can also help stretch things out and relieve soreness. Avoid hills, especially downhills, and speedwork until things clear up. You might want to take a few more weeks off running if even running on the flats is triggering it. Maybe look into whether a change in shoes, or worn-out shoes, might have caused it. Maybe your shoes' cushioning is wearing out, or they just don't have enough cushioning for your size, biomechanics, and/or the terrain you run on. You could also try running on a softer surface.

I've had persistent quad soreness once, oddly, after a climb with a really long day going down, with some technical stuff on the descent where you put your weight in weird places and go very slowly, not from run training or a race. My legs felt worse than after a marathon (it was that post-marathon level of soreness/fatigue where you're afraid you couldn't speed up to avoid a car while crossing the street, even if you had to to save your life) and it didn't resolve until over a week later after a couple of massages.