Your question about "appointment" and "switch" is difficult for me. I'd rather use some more formal verb, such as "postpone", when it is about an appointment with some important company or person, but let's stick to the "switch" problem. Others will probably provide you with some help.I too need to learn more about this verb.
Some minutes later:
I think it safe to say:"I want to switch it to two days later."
I am not sure about "forward","by" or not using any preposition before "two days".