if you haven't alreadylooked try c25k, couch to five km programs. You're a gadget guy so you could program run walk run into a Garmin.
hear what you say about walking, are you using the warmer weather to explore your area? I have been building up after sciatica bout and am running 4 or so miles in about 45 minutes through local trails by running and walking. Lots to see and am enjoying taking in new routes.
im not much lighter than you, it's all about right shoes, resting and taking your time. good luck with yr next event and you have some bottle trying that last one.
Sounds like shin splints, which you will find loads about on google.
you should rest, look up R.I.C.E.
usual things to help are calf stretch exercises, you also should have your running shoes checked at a proper running shop. I found over pronation was causing mine, now I have the right shoes I have no issues.
hope it all works out for you and well done on your 3 miles, I remember feeling very pleased when I got that milestone.