The 43-year-old former glamour model was handed a 16-week suspended sentence in December for the offence, which was committed while she was disqualified and did not have insurance.
Price was driving to visit a nearby friend in Sussex when the crash occurred at around 6.20am on September 28.
Appearing on Good Morning Britain alongside her son Harvey, she said she feels “ashamed” of her actions but that 2022 will be her year of “no dramas”.
Asked about nearly being sent to prison, she said: “They could have done and the events leading up to it were really traumatic. And it’s still been traumatic after, so I’m not ready to talk about it yet.
“But what I can say is, obviously I went to (treatment centre) The Priory. And I’ve made the decision finally that I see a therapist every week forever to deal with the traumatic events that led me up into that car. Because I’m very good at hiding things.
“But when I’m ready to talk about it, I will come on and talk about it. Because there’s reasons why I got in that car, my mental state. When I’m ready to talk about it, I’ll talk about it.
“I feel ashamed about it all and everything. But, like I say, it was all traumatic build-up to it, and it’s been traumatic after and the reasons I’m still dealing with now.
“But it’s a new year and I’m still dealing with it all. When I’m ready to talk about it. I just think people shouldn’t judge people until…
“There’s always reasons for reasons and, like I say, I am seeing a therapist each week now.”
Price also dismissed reports that she is giving up alcohol as part of Dry January.
She said: “This Dry January is from the media who have said this. This is the thing, I’m not even a big drinker anyway.
“But this year I want to be really healthy and just focus on myself, to be honest. Mental health is a massive, massive thing. But I’m excited for this year.
“I know what’s coming up, lots of good things are coming up, and I’m just going to be healthy and just continue seeing the therapist, and I’m looking forward to this year.”
Price, who has five children from three former partners, said she hopes to marry current partner Carl Woods this year and have more children.
“I absolutely hope so,” she said when asked about the prospect of a wedding.
“This is the year for me. Babies, marriage, I want it all. Like I’ve said before, I’ve definitely found the one with Carl and we will get married and it will be in England.
“It always will be in England because obviously the family (is) there and obviously my mum’s terminally ill.
“She can’t travel so I would never get married unless my mum was there as well.”
Last year, Price was given a 16-week jail sentence suspended for 12 months, a two-year driving ban, 100 hours of unpaid work, 20 sessions of rehabilitation work with probation, and was ordered to pay £213.
District Judge Amanda Kelly told Crawley Magistrates’ Court that Price already owed £7,358 in relation to previous offences.