Things to keep in mind:
1) Different sites have different rules regarding the extent of their background checks, what is and isn't an exclusion, etc. So this can vary from starting a program, to doing external practica, to working at certain internship sites, to postdoc jobs, to licensed jobs.
2) Different states have different regulations when you apply to licensure. Unfortunately, there's no easy way to find out how this would impact your ability to get licensed in any particular state without reaching out to the licensing board...and since that is a ways away from where you are now, it's hard to know if where you'd like to end up at the moment is necessarily the state you'll want to end up at in the future.
3) Even if a record is expunged, depending on the type of work you want to do, it can still come up (e.g., if you want to work in prisons or doing forensic assessments etc).
4) Even WITH all the above caveats, it sounds like the specific circumstance you describe above is pretty minor - you say you were charged, were you actually found guilty or not guilty? Were you sentenced? Was it a misdemeanor or a felony? Were you a minor or an adult at the time? Lots of details that could be relevant, but from the context you provided it doesn't sound as concerning to me as someone who had, say, a felony drug distribution charge, or any kind of charge for a violent crime.
5) I would recommend talking to an academic advisor in your major at your university to get their opinion! They might be able to help you a bit more regarding details of licensure in your state.
6) EVEN IF a career as a licensed psychologist is out of the question, there are lots of other careers that involve working with and helping people that require a master's level credential, and those may have very different background check requirements. I wouldn't say that you can't work in the field of psychology as a whole just because of this one thing, even if it might limit some of your options down the road for any particular credential or a particular position. If this is your passion, I imagine you can figure out a way to make it work! Good luck, OP!