I have pain that radiates down both legs from the sciatic nerve. Should I be worried?

Potentially yes. Visit with your doctor to determine how much you should worry. If the pain is caused from a spinal disc problem, then it can get worse. Rarely it can cause paralysis and other types of permanent damage.
No as most get . Better with no surgery if due to a disc herniation. Even if due to spinal stenosis , only 15% get worse with 15% getting better & the rest remaining the same. Other reasons for pain can be peripheral vascular disease and arthritis of the hips and/or knees. All are treatable and can be diagnosed by a physician if symptoms warrant an evaluation .