It's been a while since you posted your question and i hope that your little one has figured out when and how to fall asleep :) I want to reply though, just in case there are other desperately over tired mothers out there.
At such a young age, you can only expect a baby to be demanding, but there are a few things that you can do to help foster good sleeping habits. You have to effectively "teach" your baby to fall asleep on his or her own. I am a mom and i understand how tempting it is when they are so small to rock them to sleep, but you really are only creating more work for yourself and less sleep in the long run for everyone concerned.
Babies as young as this should not be awake for longer than 45mins at a time and should sleep for around 3 hrs when they do go down. Allowing or encouraging them to be up longer than this will only over stimulate them and make it more difficult for them to fall asleep. A good way to make sure you don't let your baby become over stimulated is to be very watchful around the 45min mark - at the first sign of a yawn, you know it's bed time. Make sure that baby is burped and has a clean nappy on and then swaddle your baby snugly. Sing them a lullaby, or rock them for 3 or 4 mins and then place them in their crib drowsy but awake! (i know this sounds crazy, but you will be amazed at how quickly they learn that it is sleep time). If baby fusses, leave him or her for up to 5 mins. If your baby starts to cry, pick him or her up immediately and soothe (cuddle/rock) until they are calm enough to go to sleep again - but are not actually asleep! Just repeat this until baby falls asleep on their own in the crib.
This method might seem like wishful thinking, but it is tried and tested and is really the very best thing you can do for yourself and your baby in those early days. There are numerous books and websites that promote this method of putting baby to bed. I think that there is a widely available book in South Africa called Sleep Sense and they too encourage parents of young babies to use this method and expound on it even more.