My gut agrees with Mamazita. Also, what do you mean by "last year?" Where are you doing your residency? Will you have your baby with you for that, or will it be another year (or several, depending on specialty) before you decide to parent?
This sound like a Lifetime movie.
However, some people have lives that sound like Lifetime movies.
So here is my answer, playing along, just in case.
I had my baby while I was in law school. I was pregnant for two semsters plus a summer, so I had plenty of time to work things out with my school. I had a place to pump, I got the school to install a diaper changing station, I had special arrangements made for the exams that happened a week after I gave birth. I found child care for my baby and arranged my schedule so I could go to school 4 days a week and have time to see him the rest of the week. I chaired two commitees, was on journal, and graduated ranked, taking no time off. It is absolutely possible.
But here is the deal- you have to re-evaluate your life plan. I was all lined up to go big firm, big salary, 70 hours a week. I spent a lot of time talking to lawyers who have children and thinking about my options. Ultimately, I decided on a career path that allows me to work 40-50 hours a week with the occasional 60 hour week instead of 60 hour weeks with the occasional 40 hour week. I have vacation time and sick time and I use them. I am able to attend my sons' school parties and volunteer in the classroom 1-2 times a year. But I made a very deliberate choice.
You are deciding right now what your priorities will be. You need to finish school, but you need to do it in a way that will not destroy your family. Can your sister come to NY and live with you for a year?
You need to look at your career path and factor in a child. You may not want to work 32 hour shifts in an ER, you may want to look very deliberately at an office practice that will let you have a set, predictable schedule.
You will learn that you have to sacrifice somewhere. Anyone who says otherwise is full of BS. You cannot be the super-Dr. House-doctor and a devoted, 24-7 mom. I chose something in between, as most of us do. It is really, really hard to acknowledge that you have to choose, but looking at the reality will help you create a realistic plan.
If I were in this situation, I would either have my sister come to NY and live with me or look at hiring an au pair who would live with me. Student loan offices would help pay for it, as awful as that student debt load would be. I would cut back on any extra curricular activities that I could and keep the class load to only what it absolutely had to be for me to graduate. Then I would work very hard to find a residency near my sister's home and an angle at a long term job in a nearby office.