I'm 100% positive if you had shin splints and you ran through it and it went away it wasn't shin splints.
From my knowledge, if you have this type of pain from just starting to run, its cause your muscles are weak. Like someone said above, strengthen your calf muscles...ecentric excersizes help...that is what one kid said, get on your tippie toes, and go down slowly...use your good leg to get on your tippie toe. also write the alphabet while your doing nothing like watching tv or in the shower.
This so called shin splint very common for someone who has just started their training after a long break.
Trust me, its not a shin splint.
Also someone posted about heat...its good to heat, but only befor your run to loosen up the muscles...than ice after....i would just stick to iceing, and get it in a cold whirl pool, not ice blocks...that way more area of your leg gets cooled.
If you want more info on this, im the man to come to...i've run many miles.
If you do truley have shin splints take a good two weeks off...also, get new shoes...shoes only last 500-600 miles. keep a log, and only run in your running shoes...dont just walk around in them...this way you know how much life you have in your shoes.
RICE is the best help for you...rest, ice, compression, elevation
no matter how hard you shake and dance, the last few drops go in the pants