Postpartum depression or very sleep deprived?

My child has given me a hard time since I brought him home. He's very colicky and fusses non stop. Brought him to see his doctor who said he's gaining weight and is perfectly healthy. I've found myself at my wits end and feeling more and more down as each day goes by. I love him but when it's 4 am and he's been screaming in my ear for hours and hours... I find myself wondering if I'm cut out for this. I feel like I'm the worst mom ever. I don't know what I'm doing and he's always inconsolable. This is my first baby and everyone says it gets better, I just wish I knew when that would be. It doesn't help that I'm so sleep deprived. My husband helps out but I am still so drained. Anyone else in the same boat?