When they were still at Raycane's palace and about to get on the carriage, Elennora could get into the carriage by himself without waiting for anyone to help him. He wasn't a girl, and he didn't need any help getting into the carriage even if he was wearing a dress.
It was intentional as he didn't want to give Levan or Davier a chance to offer him help because he knew that he shouldn't accept either of them. Accepting Levan would only anger Davier, and accepting Davier would only annoy Levan.
The two men would probably fight again if that happened, and that was why Elennora quickly boarded the carriage by himself without waiting for any help.
Unfortunately, he was too late to react when the carriage finally came to a stop, and before he could get out of it, the two men left the carriage ahead of him, and now they were offering their hands to help him out of the carriage.