Is my wisdom tooth infected?

Sounds like it might be but you will need to get your dentist to check it out.Its not an emergency so keep your appointment.In the meantime,keep it as clean as you can and use a mouthwash.Try a different one like corsodyl which you can get from the supermarket or chemist. A good tip is to dip a cotton bud in the mouthwash and clean around the sore gum with it after brushing your teeth as it wont hurt as much andwill keep it cleaner.Take painkillers if its really sore.The problem takes 7-10 days to settle but may come back again until the new tooth comes through.It will settle don't worry.