The error message I was getting stated:
"Cannot find wrapper assembly for type library "EnvDTE100". Verify that (1) the COM component is registered correctly and (2) your target platform is the same as the bitness of the COM component."
After Googling, I found from this site that if you install Visual Studio 2017 on your machine, it will affect your references to the EnvDTE assemblies. I had recently installed VS 2017. Thankfully, the site also contained the solution:
"In old VSIX projects: Remove old COM references to EnvDTE, EnvDTE80, EnvDTE90 and EnvDTE100. Add new references using Assemblies | Extensions tab and select EnvDTE, EnvDTE80, EnvDTE90, EnvDTE100. The project should build now."
I updated my references and everything started working again.