If I Have Three Months Left On My Contract Can I Upgrade?

Well I Have a Iphone 4s and my contract is suppose to end this year. Anyways I Still Have Until December 22 Until I Can Upgrade. I dialed that *639# Number and it said I could but I don't wanna by a phone if it cancels my current one. So will I be okay and not charged $36 Dollars Again?

Added (1). Thanks, But I don't wanna Trade In The Phone Because I Wanna Keep It as a backup phone just in case.

Just take it to your carrier store and they will switch it for you. You can then sell your 4S also or trade it in as apple now takes trade ins.