Hiya, as mentioned there is a parent forum which you might find useful here:
https://www.diabetes.co.uk/forum/category/parents.16/
I was diagnosed as a teenager, so a different situation, and I know many find pumps extremely useful but I've always found the idea of them more restrictive. I guess I was lucky in that I have always responded well to injections. I also have a libre sensor as mentioned above. Each CCG now has to prescribe these to at least 20% of their diabetic patients so it is easier to get on the NHS, but I know many self fund the sensors while they are waiting for it on the NHS prescription. While you're waiting for the NHS script where you get a free meter, you can use a smart phone to scan the sensor. It will tell you the glucose readings over the last 8 hours. I'm not sure if there is anywhere to order the libre 2 sensors in the UK yet but these also have Bluetooth function so it can be set up to send readings to your phone more like a CGM. I've read about libre 2 being available in Germany for a little while.
The early days are scary for everyone so do keep asking questions! It is possible to live a very happy unrestricted life with type 1, so while there will be ups and downs, there is no reason why any diabetic should not be able to live a full and happy life. There is a lot to learn at first, but in a weird way I am glad I can inject as at least I don't have to restrict what I eat! The injections and glucose tests are there to help us live our unrestricted life, so I feel fortunate I have these to help me. I know they weren't around that long ago so feel fortunate for the advances in technology to allow me to live.
While overall you want to aim for stable blood sugar levels, the early days are hard while there is so much to learn. It is normal for the levels to be fluctuating in the early days. A short period of slightly higher levels are so very very unlikely to cause any long term effects, that this might be something to discuss with the diabetes team to allow for less sleepless nights. I remember my paediatric DSN scaring my mum that my levels had to be exact all the time, but her worry was not worth it. A night where my readings are 8-10mmol but everyone has slept well is better than lower readings but sleep deprivation. Diabetes is never the same for any two people, and so it is also important not to compare to other diabetics.
We all have days that are easier than others. The early days are a steep learning curve so hopefully other parents will answer but hopefully the thread will also help you. It will settle down for you all