Pain in right shoulder and neck and its been six days since appendectomy is this normal?

May not be related: Appendectomy surgery would not likely be related to shoulder and neck pain. Was the surgery laparoscopic? Sometimes there can be transient right shoulder pain after laparoscopic surgery, but not usually neck pain, and usually would not last for 6 days. Contact your surgeon for an examination.

Probably yes: I assume you had a laparoscopic appendectomy. In such a case, the abdomen is inflated with co2 gas to make a "cave" that the surgeon can see/work in. At the end of the case, the co2 gas is removed, but invariably, some remains beneath the diaphragms. The "pain" nerves of the shoulder are the same as the diaphragm. Therefore, patients often complain of shoulder pain after laparoscopic surgery.