My understanding of NFC is that, as a standard, it doesn't offer any provision for encryption of data security.
This means you'll have to implement security on top of it.
So first: the important part: do not try to implement it yourself:
- You do not have the understanding necessary to design it properly (as demonstrated by your question)
- Even with proper design, implementing security properly is a hard problem even for experience programmers and designers
- There are plenty of libraries (starting with OpenSSL) that will provide you with the necessary tools for the task, are scrutinized by the best minds in the business for potential weakness and issues (even if old implementation bugs surface from time to time).
Now for the specific part of your question: AES is a bloc cypher. In itself, it does not provide with either authentication or data integrity. All it does is describe how you can use a key to encrypt a single fixed size block of data. You need to couple it with a block cipher mode of operation to add the properties necessary to make it useful in practice: apply it on arbitrary length steam of data, protect against replay attack, data modification, authentication, etc. All these properties depends on the mode of operation you pick.