Did the furniture store give you a W-2? A 1099? If not, then you didn't work there. If you already put it on your resume/job application and there is no paper trail, which leaves you 2 unpalatable choices. You and the furniture store are dodging taxes, or you falsified your application. If the furniture store confirms your employment & you made < $600, then there is no foul. If you made > $600, but less than the amount to file a return, then you may be off the hook, although the furniture store may not. If your employment was just last year and this year, then you still have time to recover.
Simple answer,...
get your taxes filed for the furniture store income pronto,...
if already done, show them your filings,...
if not already done, you will likely find out you owe taxes plus,...
you are not liable for what the furniture store did or did not comply with,...
you do not run their books, you only run your own,...
your new job in the well paying nuclear sector will help you with your tax bills,...
any tax dodging on your part, perceived or actual, is a trustworthiness issue,...
and can allow the utility to stop your application cold,...
your choice from here on,...