It's hard to say definitively if your feet are the source of your problem but if you think they are there might be some things you can do. First of all, you are a supinator. Most supinators strike on the lateral side of the heel and toe off at the big toe. This sounds like what you do and this foot strike pattern is pretty normal. The good thing is that many top level sprinters are supinators. The bad thing is that if it is extreme it can lead to problems. Here's a couple things to try:
1. Strengthen your feet and ankles by walking barefoot in sand, running barefoot on grass, and doing foot exercises with a towel, a partner, or isometrically.
2. Check and treat for adhesions in your foot that may worsen your problem. If you have a very high arch, run your thumb hard in the arch to see if there is a lot of adhesions and scar tissue buildup. If you feel as if there is crunchy tissue in there, get some lotion and continue to apply hard pressure to the arch to break up the adhesions.
3. In the exercises, emphasize ones that will strengthen your lateral ankle and increase flexibility in your medial ankle.
4. Never wear your shoes to the point where you see your heel get extremely worn out. This is even more true for your everyday walking shoes. You take more steps per day in these shoes than your training shoes and if your shoes are terribly worn this may cause the problems that manifest themselves when you feel pain in training.
5. Switch up shoes on a daily or bi-daily basis. This not only extends the life of the shoes but allows the tiny muscles of the feet and ankles to be strengthened in slightly different ways.
6. Consider seeing a podiatrist to see if your foot problem is indeed serious or in need of custom inserts (orthotics).