Call your cellphone provider. They may have implemented *57,
NANPA : Vertical Service Codes - Code Assignments
which allows a customer initiated trace of the last call. Usually this is uded for threatening and harrasing calls. However, you will not get the number of the trace, but it's available for law enforcement.
"private" doesn't bloct ANI or Automatic Number Identification systems. Meaning you cannot block your number when you call the police or an 800 number and even some large corporations which use ANI rather than CID (Caller ID).