Hello, babydoll! I'm not a medical professional, just the parent of a kid with diabetes. Different insulins have different peaks, they take different amounts of time to take effect, and they wear off at different rates. I suspect that is what you're seeing.
Apidra takes effect in 10 - 15 minutes, peaks in 30 - 60 minutes, and is gone within 4 hours. Levemir takes effect in 3 - 6 hours, peaks in 6 - 15 hours, and is gone within 18 - 24 hours. It is possible your Levemir dose is gone before you expect it to be, which is why your scores are now higher in the morning. Consult your endocrinologist about possibly changing the time that you take the Levemir, as that could change your scores. Mornings typically are high blood sugar times anyway, because of the simple acts of getting up and going, so if your long acting insulin isn't there to help you, that would certainly explain your scores. Good luck.
RL has given you sage advice. I agree with it. If changing the time of your injection according to your doctor's suggestion (after you talk to him) doesn't help, you may want to ask your doctor if there is a type of insulin that will match your body's routine better. There are many available types, and all have slightly different peak action and length of duration times. There may be one that matches your own body's clock better. We wish you the best.