Or do I need to start fresh?
According to the documentation: Followers, yes; posts, no.
https://docs.joinmastodon.org/user/moving/#export
https://docs.joinmastodon.org/user/moving/#moveThere is a migration function in the preferences
Mastodon supports account migration. You can export the list of your followers and the accounts you follow as CSV and import them from another instance. But there’s no option to import posts yet.
Also, note that when you migrate all followers in the old account will get automatically unfollowed.
For more details, see https://docs.joinmastodon.org/user/moving
As others have said: followers yes, posts, no. Some other Fediverse platforms can migrate posts, though, and I believe Firefish (previously known as Calckey) is able to import posts from Mastodon as well as from other instances of itself.