The reality star, 43, crashed her car in West Sussex in September and was sentenced this week, with district judge Amanda Kelly saying she "could have easily killed somebody".
Breaking her silence on Instagram, Price apologised and said she was so grateful that nobody was hurt in the accident.
She told fans she was now spending time getting better and dealing with her mental health.
She wrote on her Instagram Story: “I would like to thank my family - my children, my mum, dad, sister, brother, my partner Carl, Leigh, and my friends who have supported me throughout these past few months.
“It’s been a really difficult time and I’m incredibly sorry for my actions – I’m sincerely grateful nobody was hurt – I realise the damage my actions could have caused not only to another family, but to my own as well.”
Price went on: “I’m now spending time getting better – mental health is a hidden illness and can strike at any time.
“The triggers that cause my anxiety and behaviour are something I’m trying to understand, come to terms with, and learn to control moving forward.
“This will be a long process for myself and something I’ll continue to work on for the rest of my life.
“It’s also something I can work on with my family so we can progress on a new chapter together.”
The mum-of-five thanked her fans for all the “messages of goodwill” that she had received.
“I’m going to surround myself with my loving family and friends and continue doing the work I love as it brings me enjoyment and helps my mental health,” she said.
“Thank you everyone.”
Watch: Katie Price has avoided prison after drink-driving arrest