Can InDesign create a non-square text box?

Yes, it can. Draw the shape with the pen tool, and then under the Object menu, choose Content>Text.

Sure, you can use the pen tool, or the polygon tool, to draw any shape you want, then click into it with the text tool to fill it with text. Since you were trying to do it with Acrobat (????) I suspect that you may not know how to use the pen tool. It's not obvious how to use the Pen tool, especially if you need to draw the shape of the state of Utah. But if you do know how to use the pen tool (experience in Illustrator?) then you can convert most kinds of frames to text frames simply by clicking into them with the text tool - which by itself can only make rectangular frames, as you've already learned.

It might be useful if you told us a little bit more about what you were trying to do; it sounds like you might be new to Adobe apps entirely, so we might be able to offer better guidance if you were to go into more detail. It sounds to me like perhaps you already have a PDF to which you are trying to add a Utah-shaped text field, which is pretty much impossible to do with any application, as PDFs are supposed to be a final target format, and aren't really meant for editing. If you are preparing a new document to export a PDF for a professional printer, then InDesign is by far the best tool for you to be using. On the other hand, if you have no experience with page layout tools, you may find the steep initial learning curve of InDesign to be daunting.