Welcome!

YES, neuropathy can certainly come on suddenly and spread to full body in a short period of time. It's this rapid onset that usually points doctors in particular directions. Diabetes is usually a slow onset, so not surprised this has been ruled out. The two things that come to mind with rapid onset is toxic neuropathy (many antibiotics can cause this) and autoimmune process. Of course, trauma would cause rapid onset, but you don't mention any injuries.

Have you taken any antibiotics lately? If so, which ones? Have you taken anything else new (Rx or otherwise)?

Do you have any other symptoms that may be autoimmune in nature? These would include, rashes (on the face or elsewhere), profound fatigue, weakness, joint pain, dry mouth/eyes, GI problems. Any symptoms that are out of the ordinary for you (sometimes it's little things like this that help provide answers)?

The EMG is an appropriate next step. But more labs for autoimmune disorders would be a good idea.