How do I stop the plan holder from seeing my text messeges?

Ask if she has digits installed on her phone. That the only way she can read them.

It may be time to get your own account.

Switch to Signal https://signal.org/en/

acckmed wrote:

I have been on my parents plan for a couple of years now. Recently she started coming at me about some text messages that she wouldn't have known about unless she read my messages through my phone. Is there a way for me to stop the plan holder from seeing my text messages or call logs?

Im not sure there is a way to unenroll from the DIGITS feature. If you cannot - then I would start using a texting app or second number app for times/ topics/ convos that you want kept private.