

Some stretches leave you with nothing spare at either end of the day. Work is relentless and takes everything you have, and then the night, which used to be when you recovered, is broken by a baby who needs you too. When there is no point in the day where you get to refill, it is no wonder you feel completely wrung out.
Feeling burnt out is not only about how much is being asked of you, it is also about how much chance you get to recover, and right now both are working against you. The demands are high from work and from a new baby, while the sleep that would normally help you bounce back is broken night after night. With the usual reset missing, it makes complete sense that you are running on empty, and that says more about the situation than about any failing on your part. It is worth taking seriously, not pushing through on willpower alone.
When full recovery is not on offer, the aim shifts to catching it in whatever small pieces you can. Rest still counts even without sleep, so any chance to stop and be still is worth taking rather than filling. Even a little more sleep, or one unbroken stretch, can take some of the edge off.
You could try:
When you cannot add much recovery, the other lever is lowering what is being asked of you, and in a stretch like this that is less optional than necessary. Anything that can be dropped, delayed or handed over frees up a little of what you have left for the things that cannot wait.
You could try:
This is far too much to carry on your own, and you are not meant to. Sharing the load with anyone who can take some of it, at home or beyond, is one of the most useful things you can do right now. It also helps to let someone know how stretched you are feeling, whether that is a partner, a friend, or someone you trust, since saying it out loud often lightens it a little and opens the door to support.
Two things are true at once here. This is a genuinely hard season that does ease as your baby's sleep settles, and it is also a real sign that you are stretched too thin and deserve support while you are in it. Being this tired is not a weakness, and looking after yourself through it, and letting others help, is not too much to ask.