How to stop my iPhone sending iMessages to another user?

You're going to get a lot of unexpected calls as you've just given your numbers to a bunch of random people....

It's likely that your devices are all using the same Apple ID. You, and mom, each need your own on your own devices. This guide should help: https://support.apple.com/guide/iphone/set-up-messages-iph3d039b67/ios

First of all you should probably delete the numbers you just exposed…

about the problem, if it happens with other apps as well, for example: you download smt on your phone and it downloads on hers as well, the problem is probably that you are both sharing the same Apple ID for both phones