The 41-year-old was shot and stabbed to death in Birstall, West Yorkshire on 16 June.
Her killer Thomas Mair, 53, was jailed for life in November after being found guilty.
In her first in-depth interview since her older sister was killed, Kim Leadbeater said it was a "whole new reality we have to adjust to".
She said: "You think things like this never happen on your doorstep. From that day on our lives have been changed forever.
"There was not really much else in my life that could have been worse."
Mrs Cox was MP for Batley and Spen and a mother of two.
Ms Leadbeater said her family and that of Mrs Cox's husband Brendan had become "closer and stronger" than ever before.
She said: "We are focusing on creating something positive out of what has happened.
"It's a whole new reality we have to adjust to and, given that, we're doing well.
"Ultimately Jo would want me, Brendan, our parents and, particularly, her children, to be healthy and to be OK."
Thomas Mair: The man who murdered MP Jo Cox
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Ms Leadbeater said her sister chose politics "as a way to do good and make a difference".
She added her family plans a memorial, including a "Great Get-Together" on 17-18 June, to bring "positivity and cohesiveness within our communities".
She said: "It's stepping beyond that divide [politics, religion], people coming together to celebrate what we do have in common.
"It's not remotely about politics, this is about people and bringing people together."
Mrs Cox was on her way to a constituency surgery a week before the EU referendum vote when she was attacked by Mair in front of two assistants and shocked constituents.
He used a sawn-off rifle and dagger and shouted "Britain first" during the attack.
He then turned on 78-year-old Bernard Kenny when he tried to intervene.
During his trial, Mair was said to "admire" Nazism.
Prosecutors said he was motivated by hate and his crimes were "nothing less than acts of terrorism".
The sister of MP Jo Cox has spoken of the effect her murder has had on their family.