Well, "normal" is a relative term. Yes, it is "normal" for new runners who engage in TFFFS (Too Fast, too Fast, too Frequently, too Soon) to get shin splints, however, shin splints are a bad thing and should never be considered "normal".
Of the folks I've coached who've had them and then gotten past them, it is pretty much a 50-50 split between those who've had to quit running for a time and those who've been able to slow down until they heal.
The advice I offered in this post is something which might help you: http://community.active.com/message/1385016#1385016