Hi Zoe and welcome to the forum. You may need to visit your doctor before losing any weight, as your body is having trouble processing protein. They should be able to advise you or at least refer you to a dietician(?) who will be able to give you some tips.
I personally, choose to just eat as healthy as I can 95% of the time. Instead of fatty takeaway, I will have a lean cuisine meal with added veges. I cook all low fat meals and have salad rolls, sandwiches and salads etc for lunch and usually cereal for breakfast. Fruit and diet/low fat yoghurt are good too. I make sure that I control portion sizes, as this can be a big problem.
Some of the girls here are on Tony Ferguson and they would be better to advise you on the protein levels in the shakes etc. (If you choose to look into the program it is something that you could mention to your doctor to see if your body could handle it).
As for how long it will take you to lose 10kgs?? That all depends on you and your body matey, unfortunately it can't be predicted. You may lose a kg a week, you may only lose 1/2kg or less per week, it all depends on your body. My doctor told me that the minimum to aim for each month is 1 kg. He said that it is great if you lose more than that each month, but if you make sure that 1kg is coming off every month, then you know that at the end of 10 months, you will be 10 kgs lighter.
Exercise is also an important factor in any weight loss. Not only will you feel great, but you will become fitter which benefits our bodies greatly.
Good luck with your weight loss journey. There are a bunch of great gals and guys on here and we are only too happy to help you get to your goal!!