I am also the opposite, but mornings are always a struggle for me in a completely different way. I struggle to wake up every day (there has only been one day in the past few months I woke up feeling refreshed) and I often am very disoriented, as if I was very drunk. I've knocked things over, sturabled, etc. It's just so hard for me to start my day! I feel extremely cloudy headed, so my anxiety is not bad, but nevertheless, it's such a pain to deal with.
I think feeling bad in either way in the morning is definitely tough. Are there specific thoughts that go on in your mind? Do you take any medication? I was taking Prozac for a while, but I took it at night rather than mornings because it was making me too drowsy (I had to stop taking it though because it was getting worse with the drowsiness- I think it was affecting my sleep, thus making me more tired with time). If you do take any medication in the morning, it might be helpful to take it at night... because with taking it each morning, it might be wearing off by the time you wake up and before you take it. Just an idea!