Please tell me you're not using in-line coded connection strings.
1: Hopefully you're using a connection string that isn't hard coded and/or in-line with your code.
A. If it is, you need someway to manage and alter that connection string via your application (have an options form or administration form)
B. If it isn't and you've made it part of settings you should have a .config file that has the same name as your exe. For example, if your application file name is WonderApp.exe then there should be a file called WonderApp.exe.config. You can carefully edit this file with notepad and change the connection string.
2. Hopefully you've been testing your application on a different computer from your development machine. You need to have a computer that doesn't have all the applications and development tools that your computer has installed. This second computer should be your QC (Quality Control) machine and it should be kept as clean as possible. (No extra applications... don't use it for a gaming machine)
When you install your app on the QC machine, you will see what you're missing from your setup package and how well your app really works in the real world. Without this machine you're just guessing your application will work. Without QC you will look bad every time one of your users discovers an error in your app.