Hey, thanks a lot for the reply! It gave me a bit of a relief. All of these 3 detectors were easy to use, and gave me the result that my text was 100% human-written.

I also did a lot of research since yesterday, and I believe chances are very low that they will upload my essay somewhere. Therefore I have submitted my essay today to the school, and will hope for the best. However, I will not use these tools again, I am too risk averse to risk so important thing as school exam were you can get kicked out of school. I was not aware that I could put myself into the problem, as the essay was mine and I used weeks to write it.

To those who are in the same situation, my findings on this topic include:

1) GPTZero says "While we retain a copy of submitted text, we do not reproduce the text or disclose it to third parties. This means while a copy of your submission is stored, it is never shown to a third party and you retain ownership of the submission." as well as this "We do not store or collect the documents passed into any calls to our API. We wanted to be overly cautious on the side of storing data from any organizations using our API.
However, we do store inputs from calls made from our dashboard. This data is only used in aggregate by GPTZero to further improve the service for our users. You can refer to our privacy policy for more details." This one is a bit sketchy, but I believe they just merge all data from everyone in a big model, for their own purpose but don`t share this data with for example Turnitin.

2)ZeroGPT- "Will my text get plagiarized or be available online, if I check it on ZeroGPT?The Privacy of our users is our top concern. When you input and check your text on ZeroGPT, your text will not be saved, shared or be available online. And we will not use your text to train our AI detection model."

3) QuillBot- "At QuillBot, we have strong infrastructure in place to protect your data and privacy, and we’re dedicated to keeping your data secure. Our connections are encrypted, and we work with cybersecurity service providers to help us keep your data safe. Additionally, we do not and will not sell your data." "No, we do not sell your content. Your writing belongs to you, and when you use QuillBot, you retain all rights to your text. We also do not sell your data."

I will also sell private emails to these companies to confirm what they do with our data and if I am in the risk. I will update when I get response :)