mistake #1 is not controlling the recruiting process yourself. If a scholarship is important, if the cost to your family is important, why on earth would you take an official visit without knowing this information in advance?
You are in control, not the college coaches. You have a list of what you want. If you want to go somewhere warm, then don't take official visits to cold places. If you want/need a certain level of scholarship, don't take an official visit until the school has committed that to you in a written document.
It doesn't matter if you are faster than the girls on the team, it matters if you are faster than the girls in the conference, regional and national level, that is one criteria for coaches giving scholarships.
Is the program well rounded or centered around a certain discipline? If it is a distance school, then they may just not want to give money to sprinters.
And if you fall for the "you can earn a scholarship later" gag, then don't hold your breath. Once you have enrolled in school and started taking classes, the power shifts to the university/coach.
Right now YOU have what they want. Your talent, so get a plan together to get what you want.