It's been a little over a week after i badly sprained my ankle and it is still pretty swollen. is this normal?

Yes: If u have never sprained your ankle before then consider yourself fortunate. Ankle sprains are very common and severe (" grade 3") sprains can take 4-6 wks. To heal. Swelling can persist even after the ligament injury has healed.Hope you heal fast!

Maybe: If pain has not reduced then you should probably see a doctor to have evaluation and x-ray.