I would decrease her dose to 0.5u and see how she does on that. I'm so glad you're on top of things - you literally may have saved her life this morning.
Always check before shooting the insulin. The insulin is typically strongest 3-8 hrs after the shot has been given, so if you can test her somewhere in that range, that would let you know how low the dose is taking her. That is very important for 2 reasons - one is that if she's going low (under 50 on a human glucometer), you can give her carbs to bring her up. The second reason is that dosing is based upon how low a dose causes the cat's blood sugar to go - so knowing that helps you make dosing decisions.
Another important thing to know about diabetic cats: newly diagnosed cats have the ability to have their pancreas heal and to become diet-controlled. That doesn't happen to every cat, but what that means is that if the pancreas is beginning to put out some insulin, the dose that was just right before can become too much. That's why cats don't just "get the right dose" and stay with that dose forever.
If you're having trouble getting blood to test, don't get discouraged. It's common - it takes about 2 weeks for capillaries to grow and then you'll get blood every time. In the meantime, your poking is stimulating more capillaries to grow. So hang in there - it's for a good cause!
Can we get you to create a spreadsheet? That is our most essential tool for helping keep track of what the cat's body is doing with the insulin. Directions for it are here:
http://www.felinediabetes.com/FDMB/...te-a-ss-and-link-it-in-your-signature.130337/
In the meantime, keep getting the preshot test and if you can, another test a few hours later and watch for any sign that she is extremely sensitive to the insulin, ie, if her blood sugar drops back into low numbers. She may have high blood sugar tonight after going so low today, but DON'T increase the dose because you're seeing high numbers. The dose is based upon the 38 that you got this morning, not the high numbers. Give the 0.5u a try and see how it does.
It would be good to post here with your preshot number before you test tonight. If it's under 200 you may want to skip the shot. Did she have ketones when she was diagnosed? Or Diabetic Ketoacidosis?