I might sound like a broken record here, but I will repeat my suggestion that I have posted many times before. I think it applies here.
Make an appointment with your child's doctor, but BEFORE the appointment, like 2 weeks or 10 days or a week (don't schedule an appointment for the next day - give yourself at least a week): start a journal.
Make several columns on a sheet of paper. Document each day in categories: your child's food that she ate and how much and at what time; the time she lay down for a 'nap' and how long that lasted; the time she went to bed and the time she woke up; and her behavior during the day (tantrums, complaining, saying she's tired, etc.). And when the undesirable behavior occurs, note what was happening. Was she being asked to do a chore? Or did she complain of being tired even when the suggested activity was a pleasant one, or something that she enjoys?
You many notice a pattern, or your doctor may notice a pattern or clues.
I have a child with a severe sleep disorder (called Non-24 Hour Circadian Rhythm Disorder, which is an autonomic disorder), who previously had 3 forms of Lyme co-infectant diseases, and who is too fatigued to literally function. She attends online school from home. I also have an older child who was a very typical, healthy child. He too would complain about being tired, but only when asked to take the trash out. Then friends would call and suggest a 10 mile hike in the mountains and he was all gung-ho for that! So that's "selective fatigue" and a bogus teen-age excuse, which of course I didn't fall for. But with my other child with the true diagnosable medical issues, it doesn't matter what the activity is. We tried taking her to Sea World, thinking maybe that getting out and having a little fun would cheer her up, and maybe she would enjoy that. However, instead of enjoying the park, she asked if she could just stay at the hotel and sleep and told me and my husband to go to Sea World without her. And this was with plenty of rest beforehand - we didn't rush the trip and gave her a whole day and night to rest and sleep before the Sea World day. She's been too tired to attend parties, family events, and sometimes sleeps more than 18 hours. Then when she wakes up she manages to crawl (sometimes literally) to the couch and needs to rest.
She has had at least 5 sleep tests of different types, some lasting one night and some lasting 3 weeks (she wore a high-tech monitor that was no bigger than a watch called an Actigraphy Unit on her wrist that monitored temperature, heart rate and sleep cycles). She failed them all. We are trying different medications and light box therapy and her doctor is wonderful.
But I sympathize with you. My child also has several other medical issues, but I really feel that along with her dietary requirements, medications, seemingly-constant medical appointments, illnesses, treatments and other problems, that the sleep issue and having a person with a true sleep disorder in the household is the most draining and frustrating for me. I know she's exhausted and it's real. But I feel like I spend a significant part of my day working around and with her unpredictable sleep habits. Planning appointments, going on errands --- it's so hard. Since she's now over 18 I got a power of attorney because trying to wake her up to answer the phone when a doctor calls, or going to pick up a document, or doing business is almost impossible, since she's only awake and alert for a couple of hours at the most in the early evening, or at 3 in the morning. Well, the world doesn't operate then! The DMV and the pharmacy and the library have daytime hours and a person with a sleep disorder does not!
So please start keeping a record of everything, and be precise. Don't write "snack". Write "1 apple and a cheese stick" or whatever. Don't write "woke up early". Write "woke up at 5:47 am". Don't write "whined". Write "was told to go outside to play but cried and said she was too tired" and note the time of day that occurred, or "was asked to put dirty clothes in hamper and whined and complained" and note the time of day. Write down your questions, your thoughts, your ideas, and tell the doctor's assistant when you make the appointment that you want time to talk, not just to have her temperature taken and a quick look at her throat, for example.
Don't give up if you think she is truly tired, and if you get a dismissal from the doctor, find another one. I was told by a school counselor that all teens are tired and to learn about a little thing called "a curfew". And this was after I presented doctor's letters explaining my daughter's fatigue and other diagnoses and after explaining that my daughter did not leave the home or even her bedroom for days and days at a time. So you might meet some resistance, or skepticism, or even criticism, but if you keep searching, you will find help and encouragement.