Can I sue a social worker for not doing her job as a counselor for my son

You can sue anyone - but the better question is what damages did you suffer, and what relief are you requesting?  It sounds like the counselor did her job, she provided some counselling, but probably not enough, and without a real plan.  Since she was hired by your ex-husband, there is also the issue of what idrection she is receiving from him.  She may be responding to his requests for counselling sessions, and if he isn't requesting any, she is not scheduling.  Instead of sueing this counselor, I would look to the court to order that a different counselor be hired, or that your ex be ordered to schedule and/or pay for more sessions, with a firm plan of action.  Good luck.