Yesterday, my mom did a general cleaning on my room and when she's done, I saw the recovery phrase of my Trezor hardware wallet on the garbage can which I placed on my computer table, I also have that same copy on my wallet but still can't stop myself to tremble in fear to lose that piece of paper. I didn't told her about it to avoid more argument because she wouldn't still understand what it is. This is what I've been scared about when people say to write your recovery phrases on a piece of paper instead of storing it online.
I would like to know how others keep these secret phrases if the people in your house are not really knowledgeable in crypto. Would it be safe if I store it online but the file is encrypted and password protected?
It is extremely reckless to keep seed-phrase on paper in the public domain on your computer desk. Of course, your mom wouldn't steal your crypto using that seed-phrase, but as you saw for yourself, she could easily let others do it out of ignorance. Someone could find your recovery phrases among the garbage (away from home), albeit with a small probability. In your case, you should take care of a safer way to store it. I would recommend that you immediately exclude the online storage option and prefer the local method. In what form it will be, paper, metal, electronic media - it's all up to you.
https://bitcointalk.org/index.php?topic=5389446.0 - here you can find some ideas for implementing your personal seed phrase storage method.