How can a patient know when it's time to consider surgery?

Depends . When there is a failure of medical management.
It depends. ."a chance to cut is a chance to cure" is an old surgical saying. Surgery has its inherent risks, depending on the diagnosis; it could be the preferred option. If the diagnosis is not emergent, seek a second (or third) opinion and explore all of the medical and surgical options before you make an informed decision.