Would you give your 2 yr old melatonin ? Please read and give me your advice ;(

So the past month it has slowly turned worse and worse and later and later. She goes to sleep around 4-6am and then sleeps until 12 in the afternoon.

It started her falling asleep around 1 and just got worse from there. It’s been about a month of this now anebimexhausted. I have a newborn so it has been extremely hard.

She will be 2 in about a month.

I took her to the urgent care last week to find out why and they made sure she didn’t have an ear infection and that’s it . The dr was not a pediatrician and prescribed amoxicillin becuase they said her throat looked red and ears looked pink but no infection and also tested for strep. When I asked why I would give antibiotics then she just said that it’s up to me If I wanted to but that I didn’t need to since there is no infection. So i didn’t since she hasn’t pulled at her ears or sounded sick.

Then yesterday I talked her dr yesterday and he just said it’s probably teething and to wake her up early everyday with lots of natural light so her body produces more melatonin and if it doesn’t work after a week or two then he would prescribe melatonin.

But after a month of doing this I’m so. Tired idk if I can do this another 2 weeks. We have tried earlier naps , no naps and nothing changes it.

Last might after taking a early nap on the day she fell asleep at 1130pm and woke up at 130am wide awake in a good mood and ready to play. She stayed up until 6am.

I have given Tylenol and Motrin thinking she is in pain and that does nothing to help her sleep. I will even try and make her stay laying down or in her crib and she will lose it until I just give up and let her play.

What would u do? Has this happened to u ?