Hilaria Baldwin

is where is thissporty located"very worried" about her husband

Alec Baldwin

.

The actor, 63, is "haunted" by the death of cinematographer Halyna Hutchins, who died last month on the set of the movie

Rust

after Alec set off a gun that should not have contained a

real bullet

, a source tells PEOPLE.

"Hilaria is very worried about him," the source says. "He is not really sleeping and just haunted by Halyna's death."

The source adds that Alec "is struggling, because he clearly understands that things are even worse for Halyna's family. He doesn't want any sympathy. He doesn't want this to be about him."

"He just wants to help Halyna's husband and child as much as he can," the source tells PEOPLE.

Halyna Hutchins

James Gourley/Shutterstock

Halyna Hutchins

RELATED:

Hilaria Baldwin Holds Alec's Hand in Solidarity amid

Rust

Shooting Fallout: 'I Love You and I'm Here'

Alec

has been in contact with Hutchins' husband

, Matthew Hutchins, and 9-year-old son Andros since the tragedy, and had breakfast with them two days after the shooting. The former

30 Rock

star told paparazzi last week that Hutchins was his "

friend

," adding that he and Hilaria have been "very worried" about Matthew and Andros.

A source previously told PEOPLE that Alec has been "

leaning on Hilaria

" and their children for support since the shooting. On Sunday, the podcast host

shared a photo of the couple holding hands

, writing in the caption, "I love you and I'm here❤️."

alec baldwin

The Image Direct

Alec Baldwin, Hilaria Baldwin

Never miss a story — sign up for

PEOPLE's free daily newsletter

to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

The shooting happened on Oct. 21 on the Santa Fe, New Mexico, set of

Rust

, a country western movie starring Alec and directed by Joel Souza. During a rehearsal, assistant director

David Halls

unknowingly handed Alec a gun that had been loaded with real bullets. Thinking it was only loaded with blanks, Halls shouted "cold gun" to indicate it was safe to use, according to a Santa Fe County Sheriff's Office

search warrant affidavit

.

RELATED:

Alec Baldwin Speaks Out After Fatal Shooting of Halyna Hutchins on

Rust

Set: 'She Was My Friend'

Alec shot the Colt .45 revolver, which left Hutchins fatally injured and Souza hospitalized.

Neither Halls nor Baldwin knew that the gun had live ammunition in it, according to the affidavit.

The investigation remains ongoing, with

production on the film halted

. No charges have been filed, though authorities have said that "all options are on the table at this point" and "no one has been

ruled out

" as they search for answers as to what led to the fatal shooting.

View comments