Yes, it is very common to feel tired when struggling with anxiety. Anxiety medications can cause you to feel tired or drowsy, and simply feeling anxious so often can take a toll on your body and drain your energy. I usually tend to get highs and lows- I'll get times when I'm jittery from being anxious, then I get really, really tired after I calm down some. Now I take 20mg of Prozac and my anxiety is pretty well under control. I hardly ever have a tough time with it now. I used to take a different medication that made me extremely tired, but didn't make me feel less anxious or any happier. Prozac makes me feel happier and less anxious, and yes it does make me tired, but only a little bit more than usual. I tend to be a pretty tired person anyway because I don't always sleep well and get allergy issues that make me feel "out of it", but Prozac doesn't make it all that worse. I take it at night to minimize the feeling as well. Xanax makes me drowsier if I ever take it (I have a prescription to only take as needed).
