Felicia Russo says her friends tell her she seems calm. But she says she’s freaking out on the inside: Her housing search is keeping her up at night.

Also part of the problem: Lately, she finds herself sleeping in a toddler bed.

For six years, Ms. Russo, 40, lived on the first floor of a cape-style house in Queens around New Hyde Park, Long Island, where she grew up. She was paying $1,400 a month for the space, but she’s been without housing to call her own ever since her lease there expired in mid-March.