Not knowing your age or anything about your past history of working out and especially cycling, I to will say see a doctor.
Us old people sometimes have issues with blood clots in our legs and that's bad news if not caught. But I wouldn't think the quads would be where you feel pain from them. I'd think the calf and the femur biceps and that other muscle group on the backside of your femur. But I'm not a doctor or healthcare professional. So don't trust me.
If you are new to cycling, I might just think you are trying to push a big gear at a 30 rpm cadence for way too long. Pedaling should be very easy most of the time. Your hard efforts should come in shorter intervals where you use a lot of power.