Unless your shoes are worn out crap I doubt they are the cause. Shin splints are parts crap shoe, doing too much and bad running form. There are videos on exercises to strengthen your shin muscles which a lot of people say worked for them.
Getting fitted for shoes is a great idea assuming the fitter isn't trying to put you in motion control shoes based on his personal bias. I have narrow feet so NB fresh foam, Hoke One One, and Alta Zero Drop fit great. For lifting shoes and everyday wear Brooks minimalist fit awesome.