I don't think it was, Ana. As I recall it was labelled 'Baby Cottingham' with the hospital name and, I think, the doctor's name. I don't recall seeing the word Thalidomide anywhere.
And yes, I thought it was odd that the doctor didn't notice that the women had that drug in common. But then again, we know about it and it's hard for us to unknow it - it would stick out like a sore thumb for us. I imagine there could have been severeal common elements between the women and this wouldn't necessarily have leapt off the page at him.