Exchange brand new iphone

You made two contradictory remarks:

1. ”Brand new” - which means purchased at an Apple Store or Authorized Apple Retailer within the last fourteen days.
2. ”Bought two months ago” - your iPhone is therefore not “brand new” and can no longer be exchanged.

Your iPhone can be traded in.

Apple Trade In - Apple

Possibly, but it wont be a straight exchange. Apple may offer a lower Trade In value since its been used for 2 months already, so you will need to pay the difference.