Hi RachelOlsen,
To address you not knowing what Family Sharing is, this document addresses that: What is Family Sharing? - Apple Support
About texting, what happens when you try? Pleases explain the issues you are having and what services you are using. I send messages between myself and another person over wi-fi with no problems. You shouldn't have to do any special settings to receive a message and you don't even need Family Sharing set up (I don't). What do you mean you have a "family account"? Are you all using the same Apple ID? Frankly I have never tried sending a message to myself but maybe that's what you're doing. It wouldn't surprise me if that didn't work. If you are using one ID, you should set up IDs for other family members:
How to create a new Apple ID - Apple Support
Create an Apple ID for your child - Apple Support