Did I underpay tax by selecting the wrong Federal filing status on my company's HR system?

Hi,

When I joined my company they used a app called Gusto to manage the HR payroll side. When I filled in the data about myself I did not know at the time that as I had just moved to the US I was classed as a Non Resident. Therefore, I incorrectly put down Married Jointly and also claimed a dependent child. I have since learned as about to do my taxes that I am a Non Resident (and will use Sprintax hopefully) and aren't allowed to claim a dependent (as I'm a UK citizen who moved from Hong Kong) and that I had to file married individually not jointly.

So my question is - because of my initial mistake have I paid/withheld too little tax by my company using the wrong tax bracket? If so, What should I do? Do I need to try and pay the tax before I file or can I just pay the owed tax after I file? If I pay after I'm wonder if they will fine me for underpaying?

Thanks,
Chris