I can't remember what any of my measurements were but in my first pregnancy (in 2013) I was diagnosed with polyhydramnios at about 36 weeks - my bump was measuring way ahead at my routine midwife appointment. I think I was measuring something ridiculous like 42 weeks when I should have been 36.
I was sent for a scan the next day and they confirmed a diagnosis of Polyhydramnios. I was sent for a glucose test to see if I had Gestational Diabetes and a further scan appointment was made for two weeks later to check the fluid again. The GD test was negative but when I went for the next scan, the fluid had doubled again and this made me nervous - I thought I might literally pop if this continued! The doctors who spoke to me after the scan suggested they might like to induce labour at the hospital on my due date rather than risk cord prolapse happening if I were at home alone and my waters broke naturally. I agreed to this but asked them to bring it forward slightly as I was feeling anxious about sitting around waiting for another two weeks. To be fair, the risk of cord prolapse is absolutely tiny in mothers with Polyhydramnios but I worried that we are quite far away from a hospital. I went in at 39 weeks to be induced and my son was born very healthy and happy. Shortly after birth they pass a tube down the baby's nose to make sure everything is clear (?), but apart from that there was nothing about my labour, delivery or post partum period that would have been any different to a mother without Polyhydramnios.
I have had a couple of friends who have had it too and they went into labour naturally and it was all fine.
Sometimes it is caused by gestational diabetes, sometimes it is caused by problems with the baby swallowing and sometimes it is just a random 'one of those things.' In my case it was the latter.
In your case, I imagine they will want to rule out Gestational Diabetes if they haven't already but you would already know by now if there any problems with your baby's swallowing as you must have had your anomaly scan at 20 weeks.
In hindsight, it caused no actual problems, just a bit of anxiety and if I were to be diagnosed with it again, I don't think it would bother me massively.
Hope that helps.
They did find it difficult to get me into established labour as the high amount of fluid makes it hard for the baby to engage properly but as I said, I know of other mothers where this wasn't an issue.