Immediately after the shooting, detectives searched her home for a gun and conducted gun residue tests on both her and the baby's father, West said, adding that the tests were negative and the search did not turn up a gun.
Citing the ongoing investigation, police spokesman Todd Rhodes declined to comment when asked about the search and those tests.
West also said she relinquished a jacket she was wearing at the time of the shooting to a detective. She told police she was grabbed or shoved briefly by the suspected shooter, and they hope to lift a fingerprint off the jacket, she said.
This isn't the first time West has lost a son to violence.
Her 18-year-old son was stabbed to death in 2008 in New Jersey, she said.
"This is the second child that people have taken from me in a tragic way," West said. "I'm so afraid to have any more babies now. I tried to raise really good kids in a wicked world."
911 calls reveal witnesses' horror
Police in the coastal city of Brunswick released to CNN three recordings of 911 calls about Thursday's shooting.
"A baby has been shot!" one woman said in a 911 call.
The exchange with the emergency operator was emotionally charged.
"Listen to me, ma'am! Is the baby breathing?" the operator replied.
"I don't know," the woman said.
She began to cry.
"Listen to me!" the operator said to the weeping woman. "We have people en route. Did you hear shots in the area?"
Yes, she heard shots, she said.
"Be calm," the operator said. "How many shots did you hear?"
"I heard like three shots. And the baby has been shot in the head," the woman said.
The woman was so distraught that she passed her cell phone to a man walking his dog.
"No, the baby is not breathing," the man told the operator.
"The baby was shot in the head?" the operator continued.
"Yes, right between the eyes," the man said, adding that he earlier heard a "small-caliber clap."
As he spoke, sirens wailed as police arrived on the scene, and the man broke off the phone call.