Should every iPhone have its own iTunes account?

I just got an iPhone 4S for Christmas, and my brother had an iPhone 4. My entire family uses the same iTunes account, and it's never been a problem before now. My laptop keeps confusing my iPhone with my brothers, and it won't let me download anything from my computer to my phone because it says it hasn't had iTunes updated, which it has. Yesterday, by brother was getting my text messages on iMessage, and I got really confused because his iPhone isn't activated anymore, he got a new phone and just uses the iPhone has an iPod. Is all this happening because we don't have separate iTunes accounts, or is there another reason?

Yes that happens. My brother and my mom share the same account and sometimes I'll reach my brother instead of my mom, or vice versa. Each phone should have their own separate accounts so it doesn't confuse it with someone else. And the iMessage still works even if its not a phone anymore. If its connected to Wi-Fi it can iMessage with other apple devices.