The problem is not likely to be true shin splints as it started related to cycling. It is likely a muscle imbalance issue. To be honest, it doesn't really matter too much either way in terms of how you manage it. The big difference is that shin splints involves inflammation and stress at the surface of the bone and can progress to a stress fracture if not dealt with properly.
I would second the shoe thing. STOP WEARING YOUR CYCLING SHOES TO WALK AROUND IN. Yes, I mean that. Those shoes are not at all designed for that type of activity and will most definitely result in some muscle irriation at the least and could get worse. So the biggest thing that I would do is bring a good pair of shoes to change in to. When I commuted a lot on my MTB I changed my pedals to platforms so I could wear decent running shoes to ride with, if I was expecting to be doing some walking.
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