Freaking out, worried my offer may get rescinded

So I recently received an offer for an internship set to start in may, but it requires a background check, which I was told is pretty extensive. My freshman year of college I received a Minor in possession charge,(alcohol) and got deferred disposition, but I never got around to getting it completely wiped from my record.

About a week ago, (2 weeks after I accepted the offer) I received a charge for public intoxication, and pleaded not guilty. I'm a junior now, and wasn't worried about my earlier charge being too much of an issue, but the repeat offense, as well as it happening so recently has me worried that my offer may get rescinded. The state I'm in considers both of these offenses to be class c misdemeanors, which are the equivalent of a parking ticket. I still haven't gone to sign off for my background check, but should I just ask the HR people if this is going cause my offer to be rescinded??? I think pending cases show up on a background check, but I'm freaking out right now so any advice/personal experience would be great for me.