The way to start this process is to wait a minimum of two years.
A 15 year old cannot be emancipated in Texas. Period. Ever. No matter what. No matter what, but-what-ifs you can think of, the answer is NO. There are no circumstances WHATSOEVER where a 15 year old can be emancipated, in your or 47 other states. No, you cannot move to one of the two remaining states and get emancipated there; the laws of your own state are what apply.
A 16 year old, in Texas, can ONLY be emancipated if they are ALREADY living outside the home, and you cannot move out without your parents' permission. So unless your parents are willing to allow you to move out ON YOUR OWN, which does NOT mean living with your best friend or your boyfriend or even your grandmother, you cannot be emancipated at 16 either.
At the age of 17, IF you can prove to the satisfaction of a judge that you have sufficient maturity AND sufficient financial means to support yourself entirely on your own (which means that you, and only you, (not your boyfriend or your best girlfriend or your grandmother or a neighbor or anyone else paying part of it) are paying for your rent, food, clothing, utilities, medical care, insurance, transportation, school fees and supplies, and all the other incidentals of life, AND that emancipation would be in your best interest (and you will need much more than, I don't get along with my mother, for that - NO teenager gets along with his or her mother) then MAYBE you can be emancipated. Then. If the judge is in a good mood.
But not now. Emancipation is not and never was intended to be a means for a minor to leave home. It was and is intended to be a means of legal protection for those teens who, through no fault of their own, found themselves living alone.