As I explained to you before, installing in your local system a bunch of drivers that you don't need is not going to help with this issue.
You must have in mind that when you deploy your app to shinyapps.io the app gets executed on their servers, not in your local machine, so it doesn't matter what you have installed in your local system.
If you want your app to be able to connect with the sql server from shinyapps.io then you have to use a connection like this, but have in mind that this is not going to work locally anymore
DBI::dbConnect(odbc::odbc(), Driver = "FreeTDS",
Database = "***", Server = "***", UID = "***",
PWD = "****", Port = 1433)