I have really bad foot/ankle pain and the bottoms of my feet feel stiff when I walk. Actually my whole body is stiff and painful but most days my feet are the worst. Went to the neurologist on Wed and was told I'm falling over because of neuropathy (even though I use a cane on the bad days)
If you are having foot pain, get yourself to a good shoe store. Forget the Footlocker, a real, privately owned sneaker store with footwear experts. I will never forget the first time I wore shoes with correct insoles that really fit my narrow feet and my high arches. It was... actively comfortable, and my feet are so much less tired at the end of the day.
So. See a footwear expert. If that doesn't work, get it checked out by a doctor.