I would like to develop an app just for my own iPhone and download the app on it, but I don't have the apple developer account. I found out that (if I'm not wrong) for an app made with Flutter it is not possible, unless I do every week some procedure. Is there some other tool like I don't know React Native or something else with which there is a way to do it? And if there is, what is that way?
You can build a native iOS app on physical iPhone device without having a paid developer account. In the past it was not possible but Apple changed that few years ago. Currently it is enough to have a free Apple ID account to build an app from Xcode to your physical iPhone device. Note that you still need to have a Mac to create native apps. Check this:
https://steemit.com/xcode/@ktsteemit/xcode-free-provisioning
https://makaka.org/unity-tutorials/test-ios-app-without-developer-account
https://frameboxxindore.com/apple/how-can-i-run-ios-apps-without-developer-account.html