Well, since you said you were one of the top swimmers in your state, I guess you have extremely impressive records.
If that’s the case, then simply fill out this form Prospective Athletes
The coach may contact you asking for videos of your practice or swim meets. Remember to stay in contact with the coach.
If the coach thinks you will be a great addition to the team, then he/she would definitely advocate for you during the admission process. This would be a huge advantage over other applicants that are not prospective athletes.
As for the recommendations, you should ask your current swimming coach (not Exeter’s) to fill out your “special interest recommendation”. Exeter’s coach could only advocate for you during the admission process, not write recommendation letters.