Tooth pain throbbing on left side. Left side molar hurts. Have a permanent retainer on the front bottom teeth, is the molar being impacted

See a dentist. Sounds like not impaction. It is dental abscess. The only way to cure a dental abscess is with dental treatment. We have now entered an era where some bacterial species are resistant to the full range of antibiotics presently available. See your dentist for evaluation and treatment. Good luck. .
No. The molar is a separate issue from a fixed lingual retainer. Go see your dentist ASAP.
Probably not. The bonded retainer should not be affecting your molar. Please have the tooth examined by a local dentist to determine the cause of your pain.
No. Retainer not related to lower molar pain. See your dentist ASAP for essential treatment.
Infection. Sounds like you have an infected back tooth, which has nothing to do with your retainer. Please see your dentist as soon as possible for treatment.