Sara, have you thought of an aupair? I worked in a town where they were widely used for people will very demanding careers. They are live in, but maybe that could be helpful for now? The demand of one infant and working night shift shouldering most of the responsibility on my own was very draining and regular nighttime care was very hard to find. My ex watched her when I worked, so my schedule went according to his and it wasn't working out when she got older. I didn't have any family help either. We did get childcare for 2 days of the week so I could sleep after a shift. It's tough.
Just a recommendation if it is something you would like to consider and can afford. You are going to burnout. You are an amazing mother and doctor holding everything together but you can't serve from an empty vessel. I encourage you to find a babysitter this weekend and just take some time to yourself.