Tess Sosa, who was aboard Flight 1549 with her husband, 4-year-old daughter and infant son, said she suffered a mild concussion during the landing, and her husband was treated for a leg injury and hypothermia. The family, from New York, continues to get hospital bills, she said. But her top priority was getting the insurer to pay for therapy to reduce the risk of post-traumatic stress disorder for her and her daughter.

Because the plane was full on the day of the accident, she and her baby were seated near the wings, while her husband and daughter were far in the rear. The plane struck the water tail-first, and water began pouring in where Mr. Sosa and daughter Sophia were sitting.

Ms. Sosa, clambering over seats toward the front of the plane with her son in her arms, looked back and caught a horrifying glimpse of her husband standing in the deepening water, trying to hold their daughter above the surface.

“I can tell you, he was looking straight at me and he didn’t even see me,” she said. Since then she has been haunted by the image, and the feeling that in her escape she abandoned her husband and daughter.

Ms. Sosa said Sophia “remembers everything. I just want her to walk away from this knowing that we did everything we could to make it make sense.” A.I.G. agents have told her that for therapy she should use her own health insurance, but it has a $3,000 deductible for mental health care.

“Why should we be paying out of pocket?” she said. “That’s why they’re there. They’re the insurer.”

Aviation insurance specialists said that an airline’s liability insurer is not normally there for medical bills after a plane crash. Passengers’ health insurance may indeed pay first  for passengers who have it  or workers’ compensation for passengers traveling on business. Later, if liability is established, those insurers circle back and try to get reimbursed from the airline’s liability insurer.

But that does not help accident survivors who have expenses in the meantime.

A.I.G. has told Ms. Sosa and other passengers that it would pay for therapy, but only for three sessions.