It also comes days after a rep for Hartwell, 38, said he wanted a paternity test for the baby girl.
The former "Cosby Show" star told Entertainment Tonight, "I have never cheated on him during my marriage. That's not who I am."
Pulliam, 37, added that getting a paternity test is "not an issue."
In fact, Pulliam claims that it was Hartwell who was unfaithful during their brief marriage.
"Early on in my marriage when I was faced with this, I was ready to leave. It's not okay," Pulliam explained. "In the process, I found out I was pregnant. And I had to take another hard look and decide if I wanted to try to work through this and forgive him for the sake of the child. Like, I had divorce papers ready."
The actress said that once she discovered she was pregnant she decided "to give him that one last chance."
Through tears, Pulliam continued, "I don't know if it's the hormones... no, it's all of it, because it's fresh. And it's hurtful. And I knew I couldn't be silent, because this isn't about money. This isn't about fame. This isn't about social media likes or follows."
"This is about my character -- my integrity as a woman being attacked -- and that's not OK," she concluded.
She later emphasized, "There's a baby in the middle of this! And regardless, if we don't want to be married, that's fine, because we agree on that. But this baby is what's important, and I feel like that's being lost."
Although Pulliam said she was blindsided when Hartwell filed for divorce earlier this week, she's ready to move on.
"There's nothing to say at this point. They can discuss that through attorneys," she said. "I have to move forward. I have to do what I need to to release the hurt, to release this, and to be happy for me and my baby girl, because the stress isn't good. The stress isn't healthy. And my only priority is her."
Pulliam and Hartwell wed in January at a New Year's party in her Atlanta home after a brief engagement.
A rep for Hartwell has not responded to requests for comment, but the former NFL player did respond via an interview with Page Six Thursday. He clarified that he actually wasn't accusing Pulliam of cheating when he asked for a paternity test.
"I can’t say she’s been unfaithful. I can say she’s stayed out, she’s not came home, she’s went out-of-town ... for three days, I don’t know what’s going on. I can say that," he explained. "I can say she wanted to get in vitro. I can say she wanted to do some things to make sure she got pregnant. I just want to make sure it is mine."
And regarding the accusations that he was unfaithful to his estranged wife, Hartwell replied, "One thing I have found out about her -- and it’s not to bash her -- is that she can tell a half-truth to make sure that she seems like, I don’t want to say the victim, but that she’s the one that’s right."