Expert opinion - should my doctor put me in inpatient treatment for cutting and bulimia?

Cutting . If the symptomology is severe enough and you are in danger of severe self harm, or death, your doctor has an ethical and professional responsibility to maintain your safety as top priority. If this means going inpatient until you are again safe which means no thoughts or actions of self harm or harm to others. Psychiatric and psychotherapeutic follow-up should also occur after being inpatient.
Some would . Many psychiatrists hospitalize people who cut and some don't. Bulimia with bingeing and purging tends to be chronic, so hospitalization is generally limited to those people who are dangerously ill. Hope this helps.