Is it normal for my teeth to be loose after wearing a retainer?

You are not wearing the retainer properly. It is meant to be worn every night. While it might be OK to occasionally skip a night, it is NOT OK to skip many nights or weeks in a row. The teeth will revert back and then the extreme pressure of reinserting the retainer will loosen your teeth. See your orthodontist and wear the retainer on a regular nightly schedule, and your teeth will re-tighten.