I Have Type 2 Diabetes And My Doctor Switched Me

I have type 2 diabetes and my doctor switched me from Lantus to Levemir and I am now having high blood sugar readings, especially in the mornings. I am taking 60 units of Levemir 3x daily. Is there a maximum amount that I can take at any one time before it loses effectiveness? I am having my highest readings first thing in the morning. When I was on Lantus and had good morning readings, I had good readings all day.