Can actual phone texting conversations be pulled up?

My friend, who is a minor, got caught with alcohol. Her parents decided to tear her room apart, and get her texting history from the phone company.
Now I’m worried that if they are able to retrieve HER side of the conversation, they will be able to get mine.
We have different phone providers, but still.
I feel like that would be a gross invasion of my privacy, as I have nothing to do with any of it, and I’ve talked to her over texting about very personal matters, none of which her parents should know about.

Phone carriers do not record phone conversations, nor do they record text messages.
They will not be able to retrieve the actual words in the message.