I thought that I was tired during pregnancy, but that was a joke compared to this. But during pregnancy you can catch up on your sleep; when you have the baby there, you can't.
Babies may start off by sleeping aorund 16 hours (if you're lucky enough to have a textbook baby; some babies sleep a lot less), but they may only sleep in 20 minute chunks. While they're awake they're demanding, and you have to be around them. When they sleep it's your job to catch up with the housework, wash bottles (if you FF), prepare for when they wake up.
They say you shoudl try to sleep when they sleep, but how can you when there is so much that needs to be done. And that's just trying to maintain a decent home, that's not even thorough cleaning. And then there's the family and friends that pop over for a coffee, when all you want to do is sleep. Then there's the lying awake at night because while your baby is sleeping, you can't, no matter how tired you are. Things don't stop just because the baby does.
And yes, you are very tied down with a baby; everything changes. You can't just pop out anymore, you have to juggle getting the baby ready around their naps, getting their changing bag ready, feeding them, then finally taking them out. There's a shop over the road from me; literally 20 metres from my house, and I would look at it longingly when I ran out of Diet Coke, because they sold it, but I found it so hard to get there.