What should I have done when I doubted sending blessings upon the Prophet (peace be upon him) during the Taslim in prayer?

Submitting from prayer is sufficient with one salutation, and its sufficient form is: "Peace be upon you (Assalamu Alaikum)." Doubt after completing an act of worship does not invalidate it. Therefore, the salutation you performed is sufficient, and do not pay attention to the doubt about omitting prayers upon the Prophet after the sufficient salutation. Praying upon the Prophet in the last tashahhud is recommended by most scholars, and prayer is not invalidated by omitting it.