My question involves criminal law for the state of: New Jersey, US Border Patrol

When I was young 14 years ago, I got pulled over for littering in new jersey and they decided to search the entire car, I told them there was a small (<1/2g) amount of schedule 1 narcotics in my pants pocket when he said it would be easier if I just told them if there was anything, they took me to the station and processed me for possession I believe, I don't have the papers anymore. The judge told them to let me go, with a promise to appear I believe. I came back to Canada and then got the letter in the mail and they had my name all backwards and my drivers licence number wrong, so I didn't even reply or go back. They didn't send any more letters after the first one.

I can only assume that when I didn't show up for court that there would have been a bench warrant in new jersey?

I have since went to the USA many times by air and have been pulled aside and processed entirely checking all my ID etc due to a person with same name and DOB who did something really bad I guess (Canadian border services send me to Immigration as well, just to make sure I'm not that guy). And they told me sorry for bothering you, this won't happen again we marked that you're okay.

Question is: would a 14 year old bench warrant from NJ (if there even is one -- any way I can check?) show up on the border services system? Maybe since they botched my name when booking me it doesn't show?

My main concern here, is that I have since gotten a DUI in Canada for a warn range blow with the new laws, and no other charges involved just the dui so from what I read I'm fine to cross the border as long as I bring my papers showing there was no other charges and it wasn't a crime of moral turpitude, So that will now show up when I try to cross the border next week. Will I be subject to a US-VISIT scan do you think (biometric scan of fingerprints) and if so would the 14 year old NJ bench warrant show up in that database? Not sure if anyone knows the answers to these questions but I don't want to end up in custody for trying to go on a vacation...