Brittany Cartwright isn't talking about her restraining order against estranged husband Jax Taylor ... but she says she's doing just fine.

Brittany was spotted out in Los Angeles Saturday in her first public sighting since getting temporary protection from Jax. She shut down questions about her ex, but had a message for fans ... "Just thanks for the support. I'm okay."

As we reported ... Brittany accused Jax of years of emotional, psychological and financial abuse, as well as physical violence, in court documents filed this week.

Among her allegations, Brittany claims Jax threatened to "gut" her "like a f***en fish" and damaged property during explosive arguments.

A judge ordered Jax to stay 100 yards away from Brittany ... and her request for sole custody of their 5-year-old son, Cruz, will be addressed separately.

Jax has denied Brittany's abuse allegations ... while acknowledging he's ashamed of some of his behavior during the height of his addiction. He says he's now 21 months sober.

Brittany isn't looking to litigate the drama on the street ... but she wants her supporters to know she's holding up.