How old were you when you were charged with the DUI? How old were you when the MIP happened?
"Expungement" will not likely be your issue. "minor" has multiple definitions under Texas law. With regard to alcohol, it can be any age under 21. In the more broad criminal law sense, "minor" is someone under 17. In some contexts, "minor" is someone under 18. It can be confusing.
Be more specific with the ages at which each of these charges occurred, what was the sentence in each case, and how old you are now for a better answer.
Whether or not you are eligible for an expunction depends on the ultimate disposition in the cases. You need to do everything possible to successfully complete the deferred disposition on the DUI. Hire an attorney if necessary. As long as the deferred doesn't turn into a conviction on the DUI, you will be able to expunge it. Similarly, an MIP and PI can be expunged upon successful completion of a deferred disposition. I would hire a ticket attorney to make sure this is all handled in a way that best protects your record.
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Under the Texas Alcoholic Beverages Code, if you are convicted only one time for an offense under that code committed while under 21 years of age, you can apply for an expungement of that particular conviction in the court which convicted you upon reaching the age of 21. Other than that narrow exception, if you receive deferred adjudication for any class C misdemeanor offense and complete the deferred adjudication successfully, you are eligible for "full" expungement once the statute of limitations expires (two years).