PHP MySQLi database object
Dont call private methods in constructor, put the code into the constructor directly (well unless you have reason to call the same piece of code from elsewhere too, not your case tho).

Don't put your db credentials into the class's constants. This way you are unable to use the class to connect to any other database. Well you can change their values, but that means change the code, or you can extend the class and override the constants. But that's also not very convenient.

You might want to prefer PDO instead of the mysqli extension. The PDO contains mysql adapter in it (maybe you need pdo_mysql extension i think). But you will have the freedom to change the underlying database transparently anytime (well unless you are using some specific sql dialect features).

PDO basically offers the same as your class does, except it has no hardcoded credentials, which, as I already mentioned, is bad.

So learn to use PDO and you may find out that you need no such wrapper at all, you just need a place where you pass the right credentials to its contructor. This place could be described as database connection factory.