Eight days later, the newborn boy was placed in foster care with one of Chicago's foremost political couples.
Foster father Edward Burke serves as a Chicago city alderman and his wife, Anne Burke, is an appellate court judge.
Now, Tina Olison says she has cleaned up her act, gotten a job as a home health-care worker, and become a born-again Christian.
A judge has ruled that the baby should be with his real mother and his older brother, who is also being returned to his mother within five months.
Olison's oldest son has been living with his maternal grandmother.
"I had went right directly into treatment and recovery right after 'Baby-T' was born, in the hopes that he would be returned to me. But it didn't happen that way. It's not going to be always that he's going to think that they're his parents, you know," Olison told CBS This Morning Co-Anchor Mark McEwen.
Olison, who now works full time as a certified home health aide, said, as part of her recovery, she went to college and got her nursing certification.
She worked in restaurant catering while she went to school and as a part-time home health aide. Olison also said she has four parenting certificates.
Olison has only been able to have supervised visits with her son, and said she looks forward to having him all to herself.
"It's going to be beautiful when it's just he and I because we'll have the chance to bond and attach to one another. Also with his brother," Olison said. "So, I think we never got the real chance that I should have gotten."
She also said the experience has taught her quite a lot about herself.
Olison said she learned "that I'm very strong. I can endure a lot of things, and that, you know, troubles will come in life, but it's how you deal with that trouble that really matters."
"I didn't revert to drugs when things got really tough for me. I kept right on fighting and kept right on getting stronger as a person, and kept fighting for what I thought was right," Olison said.
She said she can relate to how the Burkes must be feeling and will allow them to see her son.
"I know how it feels to be separated from your child, because I had been separated from mine. It's very painful."