Definitely talk to your coach and mom. Personally I would prefer pads, especially on my first period, but if you can manage tampons people say that that's more comfortable with the leotard.
I don't know when your meet starts, so this may be way too late but: there's some info in this thread: https://chalkbucket.com/threads/girl-talk.70277/
I do want to let you know: dont worry if things go a bit less well on your first period. Your stomach muscles cramp, so some gymnasts have a bit less core control (not all gymnasts have this) and it may take getting used to.
I hope your coach and mother can help you further with this, and good luck with your meet.