37 year old - just diagnosed

Breathe! I am not your age and wasn’t very skinny when I had chemo (not quite sure where your bc nurse gets her information) but if two oncologists are recommending chemo, that recommendation deserves a hard, clear think! Try writing down what scares you - so you can analyse it rather than react. Chemo can be very unpleasant, it can also be quite manageable. Reactions vary wildly and very few are predictable (fat people don’t ‘do better’ than skinny people). If you find the side effects intolerable, you can stop! I did four rounds of A/C - yes I lost my hair, but cold cap has come a long way in the meantime and you may not. My only other side effect was certainly age related (30 years more than you). I worked through six months of chemo and no, I am not some sort of workaholic martyr. I was fine. 
it is always the patient’s decision, but some identification of your biggest fears and what may be done about them may be useful at this juncture. Many of us have worried long and miserably about something that never actually happened while having treatment, we know that feeling. The aim is always the same however - a long life, cancer free. Best wishes.