My android phone UI has stopped working. If I purchase more cloud capacity from my laptop, can the cloud copy all the data on my phone without me being able to give instructions to the phone?

The way I understand it, I have to either have a factory reset done ( wipe clean the content) or buy a new phone to get the User Interface to work. I want to save as much data as I can but it turns out that my cloud subscription included in my service is the minimum. Am I "grasping at straws" ?