If you use WinAPI, it won't look as customized and your game will not be portable.
Here is the standard list of GUI APIs
TGUI2 - This API has been used in several games in the App Store. I'm not 100% sure if it has a TextBox though. I can't find a working link to its GIT repo, but maybe the developer can help.
GWEN - This API was made by the same guy that made Garry's Mod. It has some nice features for events and it's pretty easy to customize. It has a Frame and a TextBox for your needs. https://github.com/garrynewman/GWEN Main issue is it lacks documentation and support.
Agui - This is a GUI API I developed for myself and released open-sourced. It was always intended for me and my projects, so the way it does certain things is not necessarily everyone's preference. It fully supports Unicode. Every function is documented (well, almost). I've been using it for years and it works great for me. I support it a lot via a.cc forum questions. It is used in this game http://www.factorio.com/ and other projects I have seen. The thing people dislike most about it is the skinning. You have to subclass each Widget to use custom bitmap drawing on them. I wanted it this way for myself so I would have no restrictions on how things look and feel. I was also new to C++ programming when I made it The TextBox and TextField are the Widgets I spent most time in so they feel and act as close as possible to Windows' ones. https://github.com/jmasterx/Agui
There are other GUI APIs. Edgar's Eagle 5 is great, though I'm not sure what state its source code is in, he might comment. But those 3 above I think are the most common, alive ones that are ready to use.
If I have forgotten to mention an API, I apologize and will be happy to edit this post to include it.