I know what it is to have a diabetic cat. And yes, it takes a blood workup, done by your vet, to adjust the amount of insulin. It is not something that you can judge yourself. And it often takes more than one of these day long tests to get to the correct dosage.
You do know that you cannot give the insulin if the cat does not have food in its system, or the cat will go into diabetic shock. My vet said that it was better for the cat to NOT have its insulin than to have it have too much.
One of the signs of diabetes is losing weight. If the cat is eating and still losing weight it is because the body cannot process the food without the insulin. But in your case, it could be that the cat is throwing up the food.
I hate to sound like a terrible person, but sometimes when the cat gives up eating it is their way of saying "life is too hard, I need it to end". This is what happened that made me decide to let Y.Lee to go peacefully.
So it looks like you have a hard choice. Make the effort to get the cat to the vet for the crucial testing or put the cat down as an effort to comfort her suffering.
Please forgive me for sounding harsh. I mean only the best for you both.