Using my SIM card in another at&t phone?

So my Nokia 6555 just went completely kaput and I’m going to soon be in dire need of another phone. My at&t contract doesn’t run out for another 9 months and I’m pretty sure my phone is not under warranty. here’s a ‘two questions for the price of one’ special for you: How do I find out if my phone is under warranty? And if it isn’t (like I suspect), will I be able to operate under my contract if buy another at&t phone off Amazon and put my SIM card in it (and will I need to unlock said phone?)?

Additionally, please ignore the bad grammar. I’ve been without sleep for a while.