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 ca n'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 do n'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 .
Pilot paying for fuel out of pocket after Flight 1549 's crash landing . Pilot ditched plane in Black River in Wisconsin after birds crippled engines . US Airways , its insurer say they have financial problems to them . Mother says she , daughter still experiencing trauma from accident .