Lillian Seenoi said she came to Northern Ireland in 2010 following threats to her and her son's life.
She was speaking on Monday during a vigil at Guildhall Square calling for the UK to do more to support migrants.
The prime minister has said that the UK will accept up to 20,000 Syrian refugees over the next five years.
Ms Seenoi said she fled from her home in Kenya along with her autistic son because their lives were "at risk."
"I was running away from my own people who were supporting the negative tradition of the Masai people, circumcision for girls," she said.
"Both our lives were at a lot of risk. Men coming to your house with knives and spears saying that they will kill you.
"It just became too much. It was too traumatising and I just had to flee."
Lillian said she had sympathy for those refugees now making their way from Syria into Europe.
"I know what they are going through. If you can imagine where you cannot sleep because you don't have any protection," she said.
"Your children have nothing and you're living in a shadow of darkness without any hope, because everybody who is supposed to help you is against you.
"I wish one of these leaders could go and be there and stay out in the night with those Syrian refugees, walk in their shoes.
"It is so sad that we can just sit and watch when we have the power to change what is going on."
A Kenyan woman who came to Londonderry as a refugee five years ago has criticised the government for not doing enough to address the migrant crisis.