I was not sent to the 12 week test for chromosomal abnormalities due to a shit GP, and living in very rural Australia.
The GP's opinion was that everything seemed fine and the sickness I was experiencing and thought was unusual was normal. First baby was okay , therefore so should the second one was his logic.
Except it wasn't. And we didn't find out the baby had Edwards Syndrome till 19 weeks with an ultrasound scan, followed by a mad rush for amnio (that wasn't available in our area) in a city 10 hours drive away.
The results were heartbreaking, and to continue with the pregnancy I would've had to move away from DH and our home for it's duration , as I was at risk, and for whatever time the child would've survived for, as no hospitals near me had the facilities to care for the baby should it have survived till birth and after.
For many reasons, including our isolated location, our first child, what the ultrasounds ( 4 of them) showed and what we knew we could deal with - we chose to terminate at 22 weeks. It was awful, and worse- could have been avoided if we had had the earlier screening done.
Essentially, if you know you would be able to cope whatever the outcome - wait and see.
If not, get the screening done. There's a world of difference between at termination at 13-14 weeks, and one at 22 weeks.
It's most likely everything will be fine, but if it's nagging at you I'd do it.