Peace be upon you and God's mercy and blessings.
Grand Ayatollah Sayyid Khamenei and Grand Ayatollah Sayyid Sistani (may God protect them):
Yes, it is sufficient to refer to another authority for obligatory precaution within the legal frameworks for deviation, and deviating after completing the obligatory precaution is enough to correct the previous action.
In any case, prioritizing the right side over the left is recommended according to the esteemed Sayyid Sistani (may God protect him).
What you have done is correct.
May you be successful in all good.
Source:
Grand Ayatollah Sayyid Sistani (may God protect him): Official site: 1, 2.