How do I create a multiple choice field that allows the client to enter text next to it?

I am not sure if I understand your query correctly. If you want to let the user to add his choice other than the options provided, you may enable the Other option in the field properties. If you want to add a text field for each option, unfortunately, it is not possible with the multiple choice field. 

Let us know if you are referring something different. We will be happy to help. 

That answered it
Thank you
Hopefully you will add the capability of adding a text field with multiple
choice. For example, I am having clients list what products they use and
need a text field next to the selection that allows them to enter the brand
name of the product
...

Besides my colleague's suggestion you may also try with the configurable list widget, this guide will help you setting that up: https://www.jotform.com/help/282-How-to-Set-Up-the-Configurable-List-Widget