What version of Premiere Elements are you using on your Mac computer? Is your USB microphone a standalone or part of a USB web cam type device?
Classically the Adobe ReadMe mentions that USB Microphones do not work with Premiere Elements. Yes, I have seen a report that USB microphone would be expected to work with correct Control Panel and program Edit Menu/Preferences/Audio Hardware ASIO settings at least in versions 10 and 11 Mac.
Please see a thread from last year and its discussion on the matter.
Some have found a few USB Microphones that do work in Premiere Elements (any version), but those reports are scattered. So to answer your question
will an other usb microphone work?
maybe or maybe not is the best answer I can offer at this time.
For troubleshooting purposes, can you create the narration in a free audio editor like Audacity and then
import that narration into the Premiere Elements project (Add Media/Files and Folders) without issue?
Perhaps we can encourage Premiere Elements users versions 4 to 13 who use a USB microphone to post in your thread (for informational
purposes) the brand/model USB microphone that has worked for them.