BARCELONA, Spain — President Trump’s travel ban disrupted the plans of hundreds of people around the globe, but perhaps none more vulnerable than Sham Aldaher, a Syrian refugee girl, and her family.

Sham, now 1½, was born without an eye and with a seriously disfigured face. Following two complex operations at a Barcelona hospital, Sham is due to receive an eye prosthesis next Wednesday. Her family had then planned to resettle in the United States.

They had already completed the required interviews and cleared all security checks before the plans were blocked by Mr. Trump’s executive order to bar citizens from Syria and six other Muslim-majority countries seen as threatening to America’s safety.

“They were travel-ready, and they are now barred,” said Jayne Fleming, the head of the human rights team at Reed Smith, an American law firm that has been helping Sham and her family. Ms. Fleming and her team are now scrambling to see whether Britain, Germany or another country could instead welcome the family. “They’re distressed over not knowing what the future holds for them.”