Depression. There are two types of depression: one is a depletion of serotonin and Prozac is a good drug for that. The other is a depletion of norepinephrine (ne) and for that Prozac is ineffective. Frequently, but not always sleeping too much suggests that it is a ne depletion and a ne reuptake inhibitor such as wellbutrin (bupropion) is effective. See your docotor to rule out other causes and talk about a switch.
Sleep and Prozac (fluoxetine) The medication may, of course, be making you feel tired. If you are taking it for depression, depression itself can rob a person of energy. There may be other reasons as well, such as infection (viral for example), medical problems (thyroid problems, heart disease, and diabetes for example). Also, examine your diet and sleep patterns. Definitely ask your doctor about your fatigue, though.