Apps that work with customer accounts. I am not sure if this actually let the customer see what they upload (one would hope so)
Price depends on shopify plan - https://apps.shopify.com/customer-attribute
Free 14 day trial - 10.00/month - https://apps.shopify.com/customr
Both of the above add extra features to the customers account and one of them is to allow them to upload files to it.
This 2 below all not linked to accounts directly but are alternatives as well.
Free- https://apps.shopify.com/form-builder-by-hulkapps
Create a form page where the customer can upload the files. This gets sent over to you via email and is under the apps menu page.
Free 30 day trial - 19.99/month - https://apps.shopify.com/uploadery
Adds an upload file field to the product and appears in the order.