The versions of Visual Studio that support "Database Projects" should provide a schema comparison tool that can be used against two different "live" copies of the database (as opposed to a "live" copy and the copy that you are working on in Visual Studio.)
You don't need to create a full-blown project (although Microsoft pushes you to do so since that is really the point of supporting database projects and it does have it's advantages) just to compare a couple of databases. The comparison tool will show you what is different and can generate a script to "merge" the changes. You don't have to manually keep track of your changes and you shouldn't have to write a significant amount of code to "upgrade" your production database to match your development database.
The trick is that Database Projects support for older Visual Studios was provided as a download, while newer versions included it. Some editions of Visual Studio don't support it. They've changed the name of the feature every time they have released it, it seems. "Frankly, I have found the licensing surrounding this feature one of the most confusing things about it. They key thing is that you want to look for support of "Database Projects".
TL;DR: If you are using Visual Studio for other things, you might already have a comparison tool via the "Database Projects" feature. If you've already paid for Visual Studio, that makes the comparison tool effectively free.