Welcome to the Apple Community.
Firstly try not to confuse your itunes account with your iCloud account, they are different things and have their own Apple ID's. If you don't want to share contacts with your son, yes you should get your own iCloud account.
As for your contacts not syncing, check that contact syncing is turned on in settings > iCloud, and also check that your contacts are in an iCloud account and not an On My Phone account. You might also take a look at this User Tip, to ensure you understand the differences between the different accounts in Address Book.