Female 17 yrs with pain in her joints no swelling no rash with elevated esr what is the next specific investigation?

Depends on what: other labs were already done. Generally I would recommend a referral to a rheumatologist (joint specialist) for a further workup, which could include testing for rheumatoid arthritis and other collagen vascular diseases.

Discuss With Doctor: In order to predict any "next specific" investigatory tests, more specific info is needed: duration, specific joints involved, fever, past medical history, & more. Elevated ESR (inflammation marker) is rather non-specific as well. At minimum, more blood tests may be needed; possibly X-rays too. Suggest a detailed discussion w/ doctor since the history, physical findings guide the work-up process.

Joint pain: Well, just joint pains in a 17yo with an elevated sed rate, which is a non-specific marker for inflammation is tough. you want to rule out more specific possible causes and assure she does not have other issues such as Lymes disease, JRA, etc, etc. so see a Rheumatologist and get the full work up to be safe. Best wishes.