I agree with BreRosie---caffeine can be sneaky! I can sometimes feel the effect for several hours. And, of course, it's not only in coffee these days, but other drinks and foods, too; even some OTC products for pain. I'm not familiar with prednisone, but BreRosie is right---meds can sometimes interfere, too.
Maybe you could ask your doctor about
taking melatonin or valerian. Check to make sure there's no interaction with other meds or other issues.
Speaking of valerian, I sometimes take a product called "Calm Tabs" by Puritan Pride that contains valerian and other herbs. It does help my sleep. Another one to run by your doctor.
And then there are the flavored chamomile teas. I like the ones put out by Celestial Seasonings. Lots of good ones there! I generally have a cup or two before bedtime.
I hope you get good sleep again soon. Yes, it sure is important, especially the next day! Take care and let us know how it's going. Best wishes.
ETA: Since chamomile and valerian, etc. are herbs, this is probably obvious, but some people can be allergic. Just a heads up.