There's an activation lock on my iPhone

To remove this you will need Proof of Purchase, if you have bought it from a person directly, you will likely not have sufficient proof to satisfy Apple's requirements (This whole policy is in place to prevent stolen phones, which in principal is a great idea but sadly it seems to effect people in situations like yourself)

How to remove Activation Lock – Apple Support

https://support.apple.com/en-us/HT201441

Hope this helps.