Is the prayer of the questioner invalid because she used to add to the wording of the Abrahamic prayer in the first tashahhud, and what should she do about that?

Increasing the prayers upon the Prophet (peace be upon him) in the first tashahhud does not invalidate the prayer. As for the final tashahhud, scholars have differed regarding the ruling on praying upon the Prophet (peace be upon him): is it a sunnah (recommended act) which does not invalidate the prayer if omitted, or a rukn (pillar) which invalidates the prayer if omitted? The Hanafis and Malikis held it to be sunnah, while the Shafi'is and Hanbalis held it to be wajib (obligatory), and the rukn portion of it is "اللهم صل على محمد" (O Allah, send prayers upon Muhammad). Since a long time has passed and you have been in this situation, there is no harm in adopting the first opinion. It is advisable to master the tashahhud in the future to avoid such differences.