Fully erupted lower right wisdom tooth has infection. Dentist gave me penicillin but I do not want it pulled. What can be done? Strange feeling by ear

Where is infection? If the tooth is infected, in my opinion you need to have the tooth removed. A wisdom tooth is not worth doing root canal therapy and crown restoration unless you have missing teeth and you need the tooth to help restore your mouth. If it is the gum tissue that is infected, then trying to keep the area clean will help prevent recurring infections. Possible minor gum surgery may be needed also.
Oral surgeon. You do not say what type of infection is present. If there is a periapical abscess it will have to be drained, and then treated with antibiotics. If not entirely effective the infection may extend into the mandible and produce osteomyelitis. You need to discuss consequence of not removing this with an experienced oral surgeon. Not sure why you do not want it out.