Story highlights Police: The bodies were in a bathtub

The mother admits to the killings, authorities say

She faces first degree murder charges

There was "no reason for this," a family member says

A New Orleans mother shot her 3-year-old son, drowned her 4-year-old daughter and took a bus to a hospital, complaining of stomach pains and a headache, police said.

The children's bodies were found in the bathtub of her home Wednesday evening, the New Orleans Police said in a statement.

The mother, identified as Chelsea Thornton, 23, admitted to officers that she killed the young children, police said.

After the killings, she said she boarded a bus to a nearby hospital.

Thornton faces first degree murder charges.

A relative of the children's father was outside the apartment Wednesday as detectives worked inside.

There is "no reason for this. I just wish that we could have helped her and helped them," Nicole Hammons told CNN affiliate WDSU

Hammons said the father of the children had an off -and-on relationship with Thornton.

"He tried to help her and help their kids, and other family members also tried to help her. You can only go so far," she said.