Need help solving my almost-3 year old's issue

Ladies I've gone to you before and you helped me in another situation, so I come to you again, this time I'm terrified and can't figure out what more to do to help my daughter.

Since the birth of her baby brother 6 months ago, my almost-3-year old has slowly deteriorated in health (mainly in eating and sleep). At first when she slowly cut down on eating and started waking up crying, I thought it was psychological - that she wasn't coping well with sharing me with the new baby. But over the months it became apparent that something physical was also going on.

She has reduced her eating to almost nothing now (maybe 2 biscuits or a few bites of apple per day) and we are left relying on toddler formula and vitamins to keep her nourished (about 2 bottles per day). She is refusing to eat 99% of the time, even foods she has always loved. She was always a good eater, I had made an effort to expose her to a huge variety of healthy foods, but I'm ashamed to say that since this eating issue, I've started trying to feed her anything (even junk food) in a desperate attempt to get her eating again. I've tried to read up on what could be causing the issue, and have tried a lot of things including getting her involved in cooking/baking with me, setting up more consistent sit-down meal times as a family, eating in front of her and not pressuring her to eat, making food look nice/creatively presented, taking her out with me to spend one-on-one time, putting her in Daycare twice a week to give her some play time and interaction with other kids (since I'm always stuck with the baby, and also to see if seeing other kids eating will help the eating situation but it hasn't, she's not eating at Daycare either except an occasional nibble)... Nothing is making a difference.

She also looks very pale to me, and due to redness on the rims of her eyelids I had her tested for allergies, but everything was negative except for the common ones like dust mites and pet hair (we don't have pets, and I've made a bigger effort to keep her room and bed sheets dust-free). Someone mentioned anaemia, but the GP said they would have to do a blood test for that and he is unwilling to do such invasive testing on her unless there was a good reason. I admit I'm scared of having her go through a blood test too, so I didn't push for one, I'm worried to traumatise her more while she's so emotionally fragile at the moment. Plus her toddler milk has iron in it.

She has continued to grow in height but has lost weight all over (on the scales she has remained same weight because the height increase has compensated for the weight loss), so the paediatrician said he's not worried about the weight.
She also snores and breathes through her mouth most of the time. This made me suspect tonsils or adenoids, but paediatrician and GP said tonsils were normal size, and that they can't check for adenoids as they are too far up the nose. They did however suggest a sleep study, which I had booked for her anyway, as she has also been waking up screaming/crying every night anywhere between 1am and 5am and I wanted to know the cause of this. We have a monitor/camera so when she wakes up and stands up screaming for us, my husband (or sometimes me) go to her. She will refuse to stay in her room or be settled back to sleep, even refuses coming into bed with us, instead she just wants to go downstairs with one of us and sit in the living room. She will remain irritable and usually continues to cry without telling us what she wants or why she's crying. We have checked to make sure she's not still asleep (night terrors), but she is definitely awake. If she was scared of the dark or anything, wouldn't she want to hop into bed with us? Sometimes she will lie down on the couch and fall back asleep until 5 or 6am. I have tried changing her bed time to earlier and later, but this has no effect. Her napping is inconsistent, but the night wakings seem to happen regardless of nap time or duration, so no correlation there either.

We did the sleep study but we won't know the outcome until we see the sleep specialist dr in 2 weeks, and he won't tell me anything over the phone just to ease my mind until the appointment time.

I look at her all the time and want to cry because she looks so unwell to me, when she used to be a vibrant happy little girl. I feel like the GP (I've seen a couple of them actually) and paediatrician are not taking it seriously and think she's ok. I know my child and she does not look or behave ok to me.

She also cries on and off during the day, for odd reasons, and always seems tired.

I'm hoping the sleep study explains something occurring in her sleep that is causing her to have poor quality sleep, and that this in turn is impacting everything else like the eating issue, but what if it has nothing to do with it? The sleep study will only explain the wakings, but what if there's some other medical issue going on?

Have any of you mamas had a child go through something like this? It seems too much to be just a behavioural/psychological phase, isn't 6 months too long to just wait it out? Am I worrying too much? What should I do? I miss her happy smiley vibrant self, and most importantly, I want her eating again. This is killing me inside :(