On leg day do you stretch first, then lift? On walking day do you stretch as well? If that’s “Yes” and “No” try the same warmup on walking day.
Do you have different shoes you wear for each type of activity? Shouldn’t be shock/impact stressors, but if so try wearing the same pair for walking to see if that helps.
Do you have the same drinking pattern during both? Just because you’re not sweating during your waking doesn’t mean that you’re using up fluids. Especially if you’re outside in a much warmer environment vs. inside a moist, humid gym.
Doesn’t sound like blood clots nor (shin) splints, as those are deeper. Nor does it sound like allergies, as that’d be on the skin, from say your laundry detergent, or any grooming lotions and potions.