Can I turn myself in?

Hello, Five years ago at the age of 21 I had sexual relations with an underage 16-year-old, four and a half years my junior. Because we were in a relationship and the crime was "statutory" rape, rather than forced (i.e. there was no restraint, intoxication, etc. but rather, pressure due to the age disparity and a degree of verbal pushiness i.e. "I'd really like it if we could have sex tonight") she has told me that she is not interested in reporting any crime - indeed, she has said that she doesn't even know what legal action there would be to take and that she has moved on from the relationship. However, I know that as a rapist, I am deserving of punishment and genuinely do not wish to evade justice. It has been 5 years and most of my life is taken up with thinking about my actions. Is there any way for me to travel to Texas and turn myself in, despite the lack of interest in charging expressed by my ex? What would happen if I walked a police station in Dallas and reported myself?