insomniphobia 

Insomniphobia occurs when you are lying in bed, but you can't sleep (insomnia). When a person is insomniphobic, it means that the person has a fear of not being able to sleep. They might fear insomnia because they know if they don't sleep they will be tired the next day, or maybe they have a big test the next day. The side effects of insomniphobia include constantly checking your phone to see what time it is, restlessness, sweating, and like any other phobias, anxiety and stress.

I had a major case of insomniphobia last night. I was afraid I woudn't be able to sleep before that big test I'm taking today.

insomniphobia by asexyunicorn June 22, 2014

insomnaphobia 

The fear of being unable to sleep, the stress of which, causes difficulty sleeping

It is difficult to know which came first, insomnia, or insomnaphobia.

insomnaphobia by traumatized January 10, 2009