Both my partner and i were treated for chlamydia but after the sixth day we had unprotected sex so is it possible we got infected again?

Chlamydia: 7 days is the usual recommended time, but if your symptoms are gone; you're probably ok. I'm assuming you mean had sex with each other. If any symptoms return, have it checked out, again.

No clear answer ...: The recommended dose and instructions for treating any infections are based on the indirect evidence resulting from continual collection and analysis of available experiences, but not guaranteeing a perfect outcome. So, no definite answer can be provided to say yes or not. Hence, wait and see with repeating tests as needed. More with reality? See and ask Doc timely.