Enlarged lymph nodes under jaw and down neck. Dead tooth with infection. Root canal scheduled in 3 weeks. Should nodes go down with just penicillin?

Penicillin is good. The infection in your tooth will be controlled with taking penicillin. You can tell if your toothache has gone away. Lymph nodes may take longer time to settle down if they are enlarged due to infection. But there can also be other causes for enlargement of your lymph nodes if they persist beyond 4-6 weeks.