NEW YORK (CNN) -- Tess Sosa and her daughter have had a hard time forgetting US Airways Flight 1549's emergency landing in New York City's Hudson River in January.
Tess Sosa holds her infant son, Damian, as her daughter Sophia, 4, plays on the couch.
Sosa and Sophia, 4, have needed therapy, and the Sosas have had to pay out of their own pockets because US Airways' insurer says only three counseling sessions are covered. The family has private insurance and large deductible.
The airline and insurer say compensation to the passengers has already exceeded US Airway's obligation, adding they gave $5,000 to passengers after the incident. But Sosa said she thinks the airline is still falling short
"They have gone to incredible measures to get all of our belongings back, dry them out," she said. "However, I think in doing so, there was this huge oversight in 'Let's take care of these passengers.'" Watch Sosa explain her expectations »
Relief over her family's survival can't undo the trauma she endured after the January 15 landing, during which she had to scramble over seats with her infant son, Damian, in tow.
Water rushed into the plane as she turned and saw her husband, Martin, sitting at the back of the plane with their then-3-year-old daughter, Sophia. She recalled her husband "in shock with my daughter being held up high, the water coming in, and hoping they'd see me."
Another passenger "bear hugged" her and Damian and escorted them to the exit.
Today, Sosa still remembers how she felt that day: "the possibility, the imminent death, just waiting to see if the plane was going to plunge any further in the river."
Following the emergency ditching of Flight 1549, Capt. Chesley "Sully" Sullenberger was quickly crowned a hero for ably landing the Airbus A320 after birds disabled its engines. He made the cover of several magazines, including People, which featured him holding Damian Sosa. See other notable air accidents »
U.S. Airways hired a firm to restore and return thousands of personal items to passengers -- items ranging from boarding tickets to suitcases.
The airline's insurer, American International Underwriters Holdings, a unit of AIG, says US Airways went above and beyond its obligations because the airline is not liable in the crash and the insurers' responsibility "is to pay valid claims on behalf of US Airways as a result of its legal liability."
Commenting for AIU, Robert Hartwig, president of the Insurance Information Institute, said he concurred that the airline and insurer had fulfilled their obligations.
"We have a flock of birds flying into jet engines for a perfectly well-functioning aircraft and a crew that exhibited extraordinary professionalism in this particular incident. This is very important to recognize, but again, the liability does not exist," he said.
This is little consolation to the Sosas, whose private insurance has a $3,000 deductible. Sosa said the family still needs help dealing with the trauma, especially Sophia.
The family just received another $1,000 bill for therapy sessions.
"I expect my family to be taken care of in the very best way possible, and I don't feel like that's happening when you're balking at my claims to a therapist and you are setting limits on that," she said.