For any team sport, you are required to wear the team uniform no matter the sport. It is unlikely your coach will even have a say on whether you could wear something else. Usually whatever league you are competing in whether it high school sports, or other travel type league - they require each team to have a team uniform meeting certain criteau.
I'd suggest wearing a similar swim suit while you practice and swim to get comfortable in it. The more you wear it the more comfortable and natural it will feel. On the bright side - once you get comfortable with wearing the swimsuit, you will actually swim faster as the suit is less resitant in the water than swim trunks and a shirt.