Calorie deficit is not working

You need to speak to a different doctor. You need to be taking medication for the PCOS/insulin resistance otherwise your body can't break down fat to lose weight.

Hi. A good way to counter insulin resistance is intermittent fasting. Try starting with hours fasting:eating at 16:8. Once your body is used to that, go with 20:4. After hour 14 of fasting your body goes into ketosis which will help with the insulin resistance.

I must admit, that's something I've not tried. I don't really understand how it works and always cautious of what I read on the internet. What sort of diet do you follow when you break your fast?

Ok let's completely ignore some of the other people on this thread- fasting and eating next to nothing as well as strictly regimenting when and what you're eating is not going to help. Your body is not getting the nutrition it needs and therefore it is trying to retain as much weight as it can.
Have you tried going to bed earlier and then getting up earlier so that you can do some exercise? E.g. during exam season where I had to just day at home doing 9 hours of revision, I would always get up earlier and go for a decent walk (5k or so) just to get my body moving and get some exercise for the day- this will kickstart your metabolism and allow you to not only eat decently with proper nutrition but also be able to use some of the protein and carbs that you eat (bc from your op it seems that you are trying to eat lots of protein but you're not actually doing anything to utilise it).
I'm sorry that you have such annoying medical stuff that has made it really difficult for you that really sucks :/ I would try to stick to breakfast, possible morning snack, lunch, possible afternoon snack and dinner- eating regularly but not having to have massive portions might help to sustain you throughout the day and keep you feeling less tired? Also yes I would still recommend talking to a dietitian- this kind of thing is their job

Ok let's completely ignore some of the other people on this thread- fasting and eating next to nothing as well as strictly regimenting when and what you're eating is not going to help. Your body is not getting the nutrition it needs and therefore it is trying to retain as much weight as it can.
Have you tried going to bed earlier and then getting up earlier so that you can do some exercise? E.g. during exam season where I had to just day at home doing 9 hours of revision, I would always get up earlier and go for a decent walk (5k or so) just to get my body moving and get some exercise for the day- this will kickstart your metabolism and allow you to not only eat decently with proper nutrition but also be able to use some of the protein and carbs that you eat (bc from your op it seems that you are trying to eat lots of protein but you're not actually doing anything to utilise it).
I'm sorry that you have such annoying medical stuff that has made it really difficult for you that really sucks :/ I would try to stick to breakfast, possible morning snack, lunch, possible afternoon snack and dinner- eating regularly but not having to have massive portions might help to sustain you throughout the day and keep you feeling less tired? Also yes I would still recommend talking to a dietitian- this kind of thing is their job

I am a single parent (during the week, my husband works away from home) working full time and doing an MPhil, there's not even 10 minutes that I can take to go for a walk. I wake up at 0550hrs and go to bed at 0200hrs. I have spoken to my doctor at length and asked for second opinions but all I get told is that I should eat a keto based diet and keep taking my medication. It is hugely frustrating and frankly depressing. I was hoping that maybe there's somebody on here that may have experience of PCOS and/or hypothyroidism that could suggest something. There's lots of stuff online about either PCOS or hypothyroidism but very little of dealing with both conditions at the same time.

Just so you know, sleep deprivation also significantly hinders weight loss.

I have PCOS and hypothyroidism, so losing weight is really hard. I have absolutely no opportunity to exercise during the day, so I have to rely on my diet to control my weight. My PCOS causes insulin resistance and hypothyroidism drastically reduces my BMR. My doctor won't do anything and has been utterly useless when I've tried to talk to him about it.

I have gradually lowered my calorie intake to 750 and try to keep my carb intake below 30g. I like to eat as clean as possible, so no refined sugar, no dairy (allergy), not much meat and cook vegetable based dishes from scratch.

My daily diet is:
0600hrs - tea with oat milk
0800hrs - protein shake made with water
0950hrs - black coffee
1000hrs - broccoli and white fish
1230hrs - salad with a protein, no dressing
1400hrs - greek coffee and a couple of dates
1700hrs - zoodles and a protein (turkey breast or fish)

But despite reducing my calorie intake, reducing complex carbs and sugar, I am not losing any weight. I am always tired, skin looks awful and my mental health is rock bottom.

I am so sick of hearing that all it takes is a calorie deficit, when I am trying my hardest to reduce my calorie intake and it's still not working.

You say you cant leave your daughter alone. Take her with you on a walk

You say you cant leave your daughter alone. Take her with you on a walk

Why are you here making excuses? You want to change your life then change

You're not a healthy role model for your daughter. At all

You're complaining so I'm going to judge you. We're all trying to help by giving you advice and you're spitting in our faces, so why should we bother? Please tell me

Also: Stop using Military time. We're not in the 40s anymore

Because if I'm not losing weight with a 750 calorie diet, then my BMR must be lower. Hypothyroidism massively reduces your BMR https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4044302/

It's the 24 hour clock, it's a standard form of time.
How am I not a good role model? She needs to see a working woman who can be married and have children rather than being a mother and housekeeper like everyone else in her family. I didn't have a role model to look up to, all that was expected from me was to get married and have children. She needs to see that women can have it all, just like men.
I'm hardly spitting in anybody's faces, do you not think that I have tried many things that have been suggested? I am at the end of my tether, utterly fed up and miserable. I was hoping for suggestions of things that I haven't tried and fresh ideas on what to do.

And we all gave you ideas... Which you're ignoring

So what do you want us to do? Wave a magic wand?

Unfortunately what she is probably seeing is that her mother has taken on too much. With everything else in your life - and now a dog has appeared too - you really didn't have capacity for the Mphil. Is the husband working away a temporary thing - if yes then I would think about pausing your studies until he is back. Your OP has you not eating in the evening so it is just your daughter's dinner. Keep that simple and nutritious as she will have had hot food at school and maybe snacks at after school club. Doesn't she get breakfast at Breakfast club or is it just childcare? Leave the washing and ironing till the weekend so that husband can help.