How do I check continuity without having a multimeter to see which white wire is my hot?
Go purchase the correct tools to do the jobs safely, rigging up some makeshift test device won't solve your problems and could end up injuring or killing you so please ignore those types of answers. 

Get a basic multimeter from the hardware store please, read the instructions, and only work on confirmed dead wiring. It only takes 0.01A to kill someone and you're working with 15A-20A here.