Terry Dickson / The Morning News via AP

Authorities investigate the scene of shooting in Brunswick, Ga., on Thursday.

Two teenage suspects were arrested in a small coastal Georgia city a day after a baby was killed and his mom shot, authorities said Friday.

The mother, Sherry West, told FOX affiliate WAWS-TV that she was pushing her 13-month-old son, Antonio, in his stroller in Brunswick, Ga., Thursday morning, when two boys – described as about 10 and 15 years old – came up, demanded money and shot them.

Brunswick police announced Friday afternoon that they had arrested a 17-year-old and a 14-year-old, and that they were charging them with murder. The arrests came after SWAT teams had gone door to door, searching for clues, and police had checked local school attendance and absentee lists to see if there were any students who hadn't been at school that fit the description of the suspects.

West told WAWS-TV that the older boy pointed a handgun at her during the encounter Thursday.

"He said, 'I'm gonna kill you if you don't give me your money,' and I said, 'I swear I don't have any,'" she told WAWS-TV of the encounter. 

She said they wouldn't accept no for an answer.

"He says, 'Well, I'm gonna kill your baby,'" she told WAWS-TV, crying. "I put my arms over my baby and he shoves me. And then he shot my baby right in the head." 

Glynn County Police Department

De'Marquise Kareem Elkins, 17.

West was shot in the leg, according to local reports. Brunswick police spokesman Todd Rhodes confirmed she received a non-life-threatening gunshot wound from a handgun.

Brunswick police identified the 17-year-old suspect as De'Marquise Kareem Elkins. The 14-year-old's identity, since he is a juvenile, was not made public; under Georgia law, 17 is considered an adult.

West was the only eyewitness to the crime, Rhodes said. Residents in the area reported hearing gunshots, but didn't see anything, he said. 

"We're not leaving any stone unturned," he said earlier in the day.

In a news conference Friday afternoon, Brunswick police chief Tobe Brown said, "We're still following leads from our witnesses. We're still collecting evidence. ... We're currently serving search warrants at three locations within the city." 

Police hadn't located a weapon yet.

The baby's father, Louis Santiago, said to WAWS-TV, "Why? Why my little one? You know? You feel they could have just taken the pocketbook and go."

Brunswick is about 80 miles south of Savannah.

This story was originally published on Fri Mar 22, 2013 9:56 AM EDT