State insurance laws and insurance company guidelines differ but it is likely that your insurance rates could increase if you are ticketed for alcohol offenses such as public intoxication and minor in consumption (or minor in possession).
Alcohol offenses are typically taken very seriously by auto insurance companies. Having a driver who may operate a vehicle while being impaired can be considered quite a risk for insurance providers.
It appears that you live in Texas. Persons under 21 years of age who are convicted of the alcohol offenses, such consumption of alcohol by a minor, will receive a 30 day license suspension for the first offense, 60 days for a second offense, and 180 days for a third offense according to the Texas Department of Public Safety.
To find out how your specific insurance carrier will react, regarding rates and premiums, to these Class C misdemeanors check with your insurance agent about how your company's rating system is set up. For information on insurance laws for your state, contact your state's insurance regulatory body.