My name is Rae and I work for Shopify. I appreciate you reaching out about the type of app you're looking for, and I'm glad to help further.
Firstly though, I wanted to let you know that I moved your question onto our 'Shopify Apps' board here on the Community. That way, this topic will be easier to find for other Community members who may be looking for a similar app.
Some apps that allow customers to enter in custom text when choosing a product are:
I recommend looking over these options to see if they will suit your needs. However, it's important to note that these are third-party apps that are developed by teams who are external to Shopify, so if you have any questions about using these apps, or the billing associated with these apps, please reach out to the app developers directly for more details. You can do this by following these steps.
I'd love to hear more about the types of products you're selling and the customizations you offer. Are you creating engraved products, or custom printed items?
Let me know if you have any questions about this and I can certainly provide more assistance!