Could you be a bit dehydrated? The more you drink the more amniotic fluid can be produced, so drinking lots of water helps.
Baby can survive with no fluid at all (one of my twins did for ten weeks) but the main concern would be lung development. However, at 32 weeks, you don't need to worry about that.
I can see why doctors may be worried about cord compression, but again, my LO survived inside me for ten week swith no fluid at all.
Also, I think they may be worried about the reason there is low fluid, are babies bladder/kidneys working properly etc. I assume they have checked that though, and it's good that levels are increasing.