JC0412
Returning Member

No federal taxes were taken out on my W2 and I didn’t think it was wrong until I had already filed

This is only my second time filing my taxes. I filed through turbo tax, then went through my county, and thought I was set. However on my W2 it showed an empty box rather than a number where it shows the amount of federal taxes payed. I just assumed it was an odd “just the way taxes work” thing, and filed my taxes. Assuming that since it came through my former employer it was fine…. When I told my mom about it she thought it was strange. 
I’ve concluded that I should definitely not have filed my taxes without double checking, but I’m working to fix my mistake. I’m trying to get into contact with my former employer, so I can get a corrected W2, but what else do I need to do? 
Will I be in trouble because I filed an incorrect W2? How do I file the correct one? Is there a different correction process for the federal/state level and the county level?