Generally you have to sit out a year of eligibility when you transfer (in D1). Your current school can grant a waiver, but they are not obligated to do so--especially with another school in the conference. Have a private conversation with a compliance officer in the athletics department at your current school. You may want to say that the academic program isn't working for you at your current school, and you'll be in a better academic program at the new school.
But first, you will want to know that you can be admitted to another school, the coach will let you walk-on the team (at least), and consider you for a scholarship. With only a year (or two) of eligibility left, this may be a low priority. Even if you can score points at a conference meet and qualify for the NCAA championships, if you only do this with one year of eligibility, a coach will prioritize giving a scholarship to someone who contribute to the team longer. Talk to the coach there and an admissions officer and a compliance officer about eligibility. Until you get an admissions offer and scholarship money (possibly), you should plan to continue at your school.
Give a lot of thought to what you need to do to graduate at your current school. If you only have a year left or so, then you might be better off staying there. Your new school will need to evaluate your transcripts and have a degree completion plan for your major. They will also have a "residency requirement" for a minimum number of units completed there to earn a degree from there. (This prevents people from transferring to Stanford for their last year of college.)