Yes, you are definitely pregnant! I was so extremely tired the first trimester. I would leave work early (and practically fall asleep driving home even though it was daylight) and take a nap for 2 sometimes 2 1/2 hours. Then my husband would wake me up to eat something and I'd go back to bed after that. I don't think we went out for about 3 months until I started to feel better (of course, I was nauseous all the time as well, and much worse at night).
It's very normal and it will pass. I must say that the first trimester was the worse...it gets much better from there! But it is all worth it!!!