Measuring at 37 weeks wouldn't have worked for me, I went HUGE when the milk came in. Think Dolly Parton. It was quite a shock and I had to go out and buy a load of new tops too, as I literally couldn't get into my usual ones.
I ordered online about 8 different M&S sizes in their cotton nursing bras when DC was a few days old, tried them all on at home and kept a range of the ones that fitted. I changed size all the time in the early weeks, between one feed and the next could change hugely, so I just wore whatever felt comfy that day.
After about 12 weeks settled to a size, and stuck with it till DC weaned, then went down yet again. (At this stage just feeling morning and evening). I'm now wearing that set of bras again, at 23 wks pg.
I never got anyone to measure me beyond a bit of string for myself to get a vague idea, just went by feel.
No one else seems to like them, but I swear by the M&S two pack of nursing bras in cotton. THey wash a zillion times, the clips work well, nothing fancy about them but are great for me. I have just sent back a JoJo one that looked similar but itched like crazy when I put it on - I am quite sensitive to lace/anything not cotton around that area!