Your message history is stored on device in your app. So long as you don't remove the old account from your app (even if you just disable it) the history should remain in the app.
Contact are stored both in the app and with your old service, your app may offer a way to do automated migration (for example Gajim does) or https://migrate.modernxmpp.org/ may be an option but I don't think the latter works with chatterboxtown.
To actually switch which Jabber ID your JMP phone number is associated with you can use the bot https://jmp.chat/faq#bot and the "change jabber id" command option.