How do I check to see if my object unwrapped properly after export? To clarify: I know how to unwrap and texture a model. I know how to export an object. I know how to import an object. I simply want to know how I can ascertain the UV unwrapping is the way I unwrapped it in Blender after import in another program.

The idea is to provide models with maps for use as game assets in other programs, and I would like to know how I can make sure it works as expected before trying to sell it. Importing it back into Blender isn't a feasible solution for me, since it might read the file differently than another program. This is really the only 3D program I've ever used with any seriousness, although I have some passing knowledge from online discussion of others, and one difference I've heard about is Blender's Z-up approach. I'm concerned this, or something similar, might affect how my export will work in other programs. I'd like to make my product as plug-and-play as possible.
I would suggest making sure you have the up and forward re-assigned in the export screen, For Example in FBX export at the lower left hand side:



I would suggest creating an 'Operator Preset' once you have the right export result.
Please don't take this screen shot as the exact settings you need. You would for example have 'Selected Objects' probably ticked for what you are trying to do.

There are a range of other tools and programs to re-open the file.
You could try importing directly into Unreal Engine or Unity. Perhaps even GODOT, (Godot tutorial here)

There is also 3D model review software like:
Autodesk FBX Review

I hope this helps.