In a post to Instagram on 2 January, the Made in Chelsea star shared a photograph of the pair hugging in front of a Christmas tree.
Louise welcomed her first child, Leo-Hunter, with fiancé Ryan Libbey in November 2020.
Last month she revealed that due to “various serious complications” during labour she had spent an extended period of time in hospital.
Writing in the caption of his post, Sam said Louise’s ordeal had taught him “to never take any day for granted ever again”.
“Nearly losing my sister was one of the toughest things I’ve ever had to deal with,” he said.
“To see all the pain she has suffered, and all the setbacks she has faced, and to see her still smiling at the end of it just shows how incredible of a woman she is.
“Just to see you put on a dress for the first time in months is everything I could have asked for and more.”
Commenting on the post, Louise wrote: “Bless you, bless my whole family. Sorry for the perpetual turmoil, hopefully I will be back to old Louise soon.”
Sharing the first photograph of Leo-Hunter last month, Louise told followers that her difficult labour had resulted in the newborn being admitted to NICU, while she was admitted to the ICU.
She said that although Leo-Hunter made a “quick recovery”, she was in hospital for a month.
“In all honesty I never imagined that so many bad things could happen to me, but to dance with death twice brings a whole new view of the world – a stark reminder of how short and sacred life really is,” she said at the time.
In a later post of herself sitting in a wheelchair in a hospital gown, the former reality star thanked the NHS staff who had cared for her.
“I want to thank the room full of people who worked through the night to save my life. Many of them were called in from their family homes at an unearthly hour,” she said. “I met a lot of people with a lot of different roles and every single person is a crucial part in the cog.”