backup issue

so I have been using this authenticator app since last year and I do not have very much experience with this, but I have used it for an site which includes my important data and it cannot be accessible without those authenticated codes and recently I moved my phone to a new one and I cannot get my data backed up in the other phone and in this phone both as well, so now I am stuck with my deadlines and no data chords. I forgot to even keep the recovery codes to help me.