For toothache and dental problems, please visit a dentist of your choice. Dentists in your area can be found in the local phonebook, in the yellow pages or via the Hamburg Medical Association
https://www.aerztekammer-hamburg.org/arztsuche.html
In case of emergency, the Dentist Emergency Service can help you on 040 18 03 05 61. The dental emergency service of KZV HH is also available from 19:00 to 01:00 at Stresemannstraße 52, 22769 Hamburg (Altona).
Further information, e.g. A radius search can be found on the website https://www.zahnarzt-notdienst.de/notdienst/0/hamburg-040.php