The moving violation is a traffic infraction. Being a minor in consumption is a Class C misdemeanor in Texas, which is a criminal offense.
According to Sec. 12.03(c) of the Texas penal code, a conviction for a class C misdemeanor doesn't impose any kind of criminal or legal liability on the offender. So a conviction would not appear in the state or Federal criminal data base. By that I mean, there would be a copy of your case and the conviction filed with the court, but the conviction should not show up on a state or federal background check.
Nevertheless, it is a public record and could be found, so if you are convicted of it, you would have to disclose the matter to Immigration, and yes, a conviction could delay your citizenship.
However, you would be eligible for a diversion disposition. A diversion offer involves a period of supervision along with up to 12 hours of community service, a 30-day suspension of your driver's license, fines and anti-alcohol classes/treatment/counseling, if appropriate. You'd also be required to stay out of further difficulty with the law. If you complete your diversion successfully, the case would be dismissed and could be expunged from your record. Immigration does not consider a pre-trial diversion opportunity as a conviction. You can see this here
Just because you are eligible for diversion doesn't guarantee it, and because you are not yet a citizen, this case -- which is very minor for a citizen -- has more serious consequences for you. So you should involve a lawyer, just to ensure that your rights and status are protected best. If a lawyer gets on this right away, he could likely get you the diversion opportunity, which is the very next best thing to an outright dismissal of the charges.