The first thing I notice here is that you said you did run/walk sprints. Does that mean you were running a hard effort when you ran?? When first starting out you need to jog, no sprinting. There are a lot of great programs that are free online that are couch to 5km programs that seem to work well for most people. For eg.
Other things to consider are how are you landing on your foot... if you are heel striking with your foot far out in front or crossing over,that is much harder on your shins. You can correct this by getting a feel for a more efficient foot striking position by doing short stride, skipping drills. To correct crossing over you do 20 sec drills of jogging along a line while concentrating on making sure each foot lands on it's own side of the line. Good shoes are also important, so if you haven't already, go to a qualified store in your area and get some help with that.
Hope that helps.
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