Different competititons have different rules. Start by checking the rules for the competition you are going to, also ask your teacher or coach.
I'm going to answer this question assuming that you are in the US. Different countries have different rules.
If you are doing Pro/Am in the US, the only rule I've ever seen is no costumes for Newcomer-level events, after that it's anything goes, but even that rule isn't always in place.
If you are doing Amateur in the US, the rules depend on the competition, and also who is sanctioning the competition. USA Dance has different rules from the NDCA, and the NDCA competitions sometimes have rules that differ from each other. And then there are the collegiate competitions, which also have their own rules. For instance, USA Dance does not allow any costumes at all on the syllabus levels, and spells out what kind of things are and are not allowed. But college competitions usually start allowing costumes on the Silver or Gold level, dependig, but this varies from competition to competition. Franchised studio competitions, like those for Arthur Murray or Fred Astaire, might have their own rules too.