After you kill the first dragon & return to the Jarl of Whiterun, he offers you Lydia as your personal housecarl. However, when I asked Lydia to come with me she says, "Looks like you've already got someone with you."

I don't have anyone following me. Any way that I can fix this and get Lydia to tag along with me?

Just realized I had Farkas waiting for me at Dustman's Cairn. Maybe that's why?

Yes, that is why. You have to finish the quest with Farkas first.