I'm definitely not an expert, but this sounds a lot like what happened with my baby. Your baby's diaper output does sound great, so I agree with the previous posts that this might be both a confidence issue and perhaps a fast letdown? Have you tried nursing in a side lying position? This helped us so much and actually we still only nurse in that position.
My baby would be up for hours and hours during the day (sleeping less than my toddler!), she wanted to nurse to sleep but I had so much milk that she couldn't comfort nurse. She would just get blasted with milk spray! It took a long time for that to change, now at almost 5 months things are better.
I know how difficult the early weeks and months are, I was just there! Know that we are all here to help you.