Definitely! It's gotten better in the second trimester (around weeks 8-15 I could barely function and just slept constantly). Still though, I find that the most basic functions, like a trip to the grocery store, require a nap afterwards. I also wake up 10-20 times a night to pee or change positions, so the sleep I do get is not very restful. It's just a part of the process. Keep yourself hydrated, take your vitamins, and try to sneak in your naps when you can. Don't fight it, if your body is saying you need sleep, just give it sleep. You're cooking a tiny human in there!
Re: always tired
Now give your doc a call if there is a cause for concern i.e.: pregnancy related anemia.