Why might my feet hurt and feel stiff without having an injury and continue to feel worse over the last month?

HURT: Some of the problems that can contribute to pain (hurt) without trauma or injury include: stress fracture, tendinitis, arthritis, biomechanical malfunction while walking, nerve entrapment, circulatory problems, to name a few. See a podiatrist for history and physical evaluation and x-rays to not only diagnose the problem but also to treat the problem too.

No Injury: Stiffness could be from an old injury that finally caught up with you or arthritis is associated with joint stiffness.