My daughter is having symptoms that I'm concerned about. How can I advocate for the right testing without sounding paranoid? For the past week to 10 days, my daughter has been complaining of eye "pain", cheek pain and pain behind her ear (all on the left

Express. Express your concerns to the doctor, including the fact that you don't want to seem like a hovering paranoid parent. After a detailed history and physical the pediatrician will have a diagnosis in mind or a list of possible things that could be wrong. Additional testing or treatments will hopefully confirm the suspected diagnosis, and treatment will be initiated. If your daughter does not respond to the treatment, then you can push for more answers/additional testing. If you are still not satisfied, then ask for a second opinion. I'm sure your pediatrician will understand. Most parents are very vigilant if they feel something is wrong with their child, and will stop at nothing until they get answers. Good luck.
Why do you ask? My colleagues have answered well. Let your daughter give the history uninterrupted. If there's something you truly need to add, do so afterwards. When the plan is discussed, if you still believe that she is not being offered the "right testing", ask diplomatically, "Could we...". He/she will explain. Usually you can trust us, and remember that much health advice online is pure rubbish.
You won't. A doc who has 25 years of formal education along with years of practice develops an understanding of what tests, if any, are appropriate. This is guided by history and exam findings. If you come in with a shopping list of tests you "want" based on your desires you will be seen as paranoid. Why would you know the "right" testing. Either you trust your doc or docs or not, if not, change.
Referred pain. There can be infectious or inflammatory processes as well as muscle spasms in the neck or cranial nerves that can cause these symptoms. The pain is called referred because the patient experiences the pain in a part of the body different than the part that has the problem. Simply explain the symptoms, how long, how severe, etc in a matter of fact way and let your doctor take it from there.