I have agoraphobia, and I have the same issues. When it is at its worst, I cannot leave the house. I have a hard time being in the house too, though. Basically I'm terrified of being anywhere.
Over time as I adapt to it (as I have now, 3 1/2 years later), it develops in other ways. I feel incredibly anxious and panicky if I am too far away from home. It doesn't matter if I'm on a plane or in a car. Traveling freaks me out. I can go into stores and stuff now, and on public transit. I make it to all my appointments, most of the time.
But I still have periods where leaving my house and interacting with the world is just not possible.
Agoraphobia, in my experience, manifests in a bunch of different ways. I think not leaving the house is probably the most common...but I have been told by my psychiatrist that there are others, like the ones I have just outlined. I have also been told that in some cases it is more accurately described as 'generalized phobia' - in other words, afraid of everything.
I guess it's just one of those things where there will be different opinions.