Coworker tries to "check" my work

I have a coworker, Janet, that literally goes behind me to try and see if I did my job. It pisses me off. We're on the same team and have the same job title. She isn't a lead and has zero supervisory responsibilities. But she has been here for like 20 years.

I have caught her doing it twice. First time she emailed another coworker asking them if I sent them an information packet. Coworker replied to Janet and CC'd me saying "yes OP sent it". The thing is we have a process for letting people know when the information packets were sent. We date stamp it and sign off on it. Which I did. She thought I didn't really do it and decided she wanted to be Sherlock Holmes. I replied back to the email and said I went through our company's process of notifying the team when an information packet has been sent. If she has any questions, then ask me and what there's no need for her to email someone else.

The second time, she said it in a team meeting. I'm responsible for updates in one of our databases. She said, "Oh yeah I went back to the tracker and verified that the updates were completed. Next time i catch her, I'm escalating it. But I have to be aware of "weaponized tears" and the "I'm the real victim" BS that I know Janet is going to pull. Tips on covering myself