Jack Brennan's mother Rachel Edwards, the driver of the car, who was six months pregnant at the time, managed to escape through an open window and swam to the surface.
Mrs Edwards then dived back down to save her two-year-old daughter, Isabella, but was unable to free her son Jack without letting go of the toddler.
The 39-year-old was driving her children through Midville, near Boston, Lincolnshire, last month when the car hit a pothole and veered off the road into the dyke.
Two of Jack's friends were also in the car but managed to escape and run for help.
Today, a spokeswoman for Lincolnshire Police said there was a "live inquiry" into the crash.
She said: "There is still lots of work to be done to establish what the circumstances were and what happened.
"We will look at the causes to see if anyone was responsible. That's not to say if someone was at fault there would be any further action - that would be up to the Crown Prosecution Service. They need to get to the point where they know what happened on that day and that's an ongoing thing."
Yesterday, Mrs Edwards gave her dramatic account of what happened to the Derby Telegraph.
She said: "At first I didn't try to get out because I was in shock. But my window had been open so I managed to get out and up to the surface.
"But Jack's window hadn't been open - I told him to close it before we went into the dyke because Isabella was sitting behind him in her car seat and she was asleep."
She continued: "I saw the bottom of the car so I shoved my hands under and I felt her car seat. I pulled her out and I knew she was still alive.
"I tried to go back for Jack but I knew if I let go of Isabella then I wouldn't be able to get her back.
"I was just screaming and screaming. (Jack's friends) Tom and Dave had managed to scramble out and they went running off to the nearest house to get help."
Mrs Edwards took her daughter to safety. But when she tried to go back and save her son, she claims she was held back by paramedics who arrived at the scene.
A police officer pulled the teenager from the Citroen Xsara estate but he was certified dead in hospital.
Mrs Edwards said her last memory of her son was of him putting his hand on her arm, as if he was protecting her, when the car began to sink.
The tragedy happened at 8pm on August 19 as they were on their way to a holiday in Mablethorpe, Lincolnshire, to stay with relatives.
Mrs Edwards moved to Essex with her children four years ago but is originally from Mickleover, Derbyshire.
Jack's father, Carl Brennan, who lives in Alvaston, Derbyshire, and is separated from Mrs Edwards, said: "It is a hard thing to put into words how I feel. You don't think you would ever have to bury your child."
After the accident, Mrs Edwards and her daughter were treated for minor injuries and shock at the Pilgrim Hospital in Boston.
Isabella was later transferred to the Queen's Medical Centre in Nottingham for further treatment.
Mrs Edwards' third child, a boy, is due on November 21 - just three days after Jack's birthday.
"Jack wasn't too pleased about that when I told him because he thought his 18th birthday next year would be overshadowed by the baby's," she said.
On August 24, five days after his death, Mrs Edwards collected Jack's GCSE results.
She said: "He got Cs and Ds. That was what he needed to get into college. He might have not got As or anything, but he made a lot of people happy and that to me is more important than exams."
More than 300 people attended his funeral in Dunmow, Essex, last Friday.
Mrs Edwards said: "The nicest thing about the funeral is that people were lining down the streets to pay their respects. Jack would have loved the funeral we gave him.
"I was surprised at how many people turned up. I didn't realise he had touched so many people. I can imagine he was looking down and thinking 'What a spectacle this is'."
At the time of his death, Jack was looking forward to going to rock festival Ozzfest, at the O2 in London on September 18.
He was buried with an Ozzfest VIP pass, sent to the family by organisers especially for the funeral.
Singer Ozzy Osbourne - who is headlining the festival - also sent the family a signed ticket for Jack's coffin.
