Infection. Do not just cover up pain. See your dentist, asap.
No. The swelling is most probably from infactions associated with your wisdom tooth. You need to take antibiotics for that, only your dentist well decide what kind to give you.
Yes + Dentist visit. Agree with dr tidman. While you can take the medications you mentioned to decrease pain and swelling, you should see your dentist as soon as possible to make sure you do not have an infèction or other issue.