Is it possible for a 16 year old to have endometriosis?

Yes. Endometriosis is entirely possible in young women. If the clionical history suggests it and the pt fails to have significant improvement while taking birth control pills, a laparoscopic exploration is needed. However, be sure to have an experienced gyn minimally invasive surgeon do the surgery. The first doctor "in" has the best chance of curing the problem, so choose your surgeon wisely.
YES. Women who have endometriosis usually have it starting around age 12-13. So many 16 yo women have endometriosis. Many women under age 18 have pain symptoms that are from endometriosis and they never get diagnosed or discussed. So yes it is not only possible but fairly common.