Hi and welcome to you and Luna.
It is always scary and overwhelming in the beginning as it is all so new. We all felt like you do in the beginning. It will get easier.
You say in your signature you are feeding wet food. That is great. Is it Low carb, do you know.? We recommmend 10% or less carbs.
I see he has been prescribed Lantus insulin. That is a good insulin and he is on an appropriate dose. Not sure what you mean by saying you didn't mix his insulin before giving.........you do not need to mix or shake Lantus insulin at all. If your vet told you this, he is incorrect. Keep it in the frig and it will last much longer.
We recommend home testing the blood sugar levels. It is the best way to keep Luna safe and to see how the insulin is working in his body. It is not hard to do and it won't hurt Luna. We can help you learn to test.
I am concerned he is not eating at the moment. It is very important he is eating if you are giving insulin so at this point, any food is better than not eating. Also I see he has some kind of infection ( with the high white cell count). Has the vet put him on an antibiotic? When a cat has diabetes he is prone to ketones which can lead on to ketoacidosis which is a serious illness in cats. The 'recipe' for ketoacidosis is not enough insulin, not enough food, and an infection or inflammation in the body. To test for ketones, you need to buy a bottle of Ketostix, which you can buy at Walmarts or a pharmacy for about $10. To test you need to get a specimen of Luna's urine and then test it with the test strip in the bottle as per the instructions. Anything above a trace needs vet assistance.
So make sure he is eating something, is getting his 1 unit of insulin twice a day and drinking fluids. And get the Ketostix. I would also ask the vet if there were any ketones in his blood test or urine test when he was diagnosed.
Here is a hug

. You WILL be able to do this. The first couple of weeks are hard with the steep learning curve and everything new but it gets much better and is just a routine to follow after that.
I would recommend you start posting over on the main forum where there are lots more people who are only too happy to help and support you. Here is the link.
http://www.felinediabetes.com/FDMB/forums/feline-health-the-main-forum.28/