DOMS (delayed onset muscle soreness) is a common response to when you first start working out.
If you have gone from nothing to walking 45-60 minutes, I'm not surprised you are feeling stiff.
Keep walking (increased blood flow to the muscles actually helps the recovery process), but dial back your speed and duration for a couple of weeks - say to 25-30 minutes.
The good thing about starting off a low base is that with regular exercise, you will see your fitness increase quite quickly, and that in a few weeks you will be able to comfortably walk distances that are currently causing stiffness.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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