What are the alternatives to surgery in the case of painful gallstones? When can I choose these alternatives, if they exist?

No good ones! Once gallstones become symptomatic, meaning they cause pain, nausea and bloating, the only effective treatment is removal of the gallbladder. This will also eliminate the possibility of developing more serious complications such as infection of the gallbladder (cholecystitis), infection of the bile ducts (cholangitis), and gallstone pancreatitis. Surgery is usually a laparoscopic outpatient case.
No good alternatives. The treatment for symptomatic gallstones is surgery. Medications to dissolve gallstones work too slowly and must be continued for a long time.