I would only worry about it if you are getting really hungry before running or running out of steam during your run. If that is the case try a banana (unfortunately I can't stand them!) 2 hrs before your run or there are numerous recipes for healthier flapjacks, dates are supposed to be good too. I find eating late can be detrimental to sleep so I would eat my main meal at a slightly earlier lunch time then sandwiches or soup about 2.5hrs before running. This works for me on days when I go to Spinning then Swim to Fitness in the evening. It is all about finding what works for you because every body is different.
I know you don't want to hear this but I would recommend starting with run/walk again and building it back up gradually. Did you see a physio or take a look at your shoes? Maybe barefoot isn't for you. I would run/walk again and build it up, perhaps you could mix it up with some cross training and some conditioning exercises to see if that helps prevent the shin niggles. If not you may need to try some different shoes, go to a running shop and see what happens.
I would suggest starting with Couch 2 5km, this programme (available on a handy app on your phone) gets you going on a run/walk programme. This is the best way to build up without hurting yourself and don't be afraid if you need to repeat a week. In the meantime just try to build up some fitness by walking, walk to the shops or the park and chase your children round the park.
You don't need equipment to cross train, there are loads of videos of different length classes on YouTube which need no equipment.
I have had my gait change due to strengthening my core (and it is happening again as I get stronger after having a child) so it is possible. I knew that something was up as I was getting a few niggles when running. I would first of all ask your physio for advice (that is what they are there for) and then go to your local running shop and get your gait analysed.