If the birth took place in one county and adoption in another, check both counties. Legal librarians may be able to assist you. Note that in many states no notice was ever published. If there was any question regarding the birth dad seeking custody then there will be something published. In later years when father's rights became an issue, the notice was published.
Church records Catholic priests or archivists can be helpful for Catholic born adoptees.
Up until about 1970, if there were at least a few months between the time of your birth and adoption you may have been baptized before the adoption. The baptismal record, which would not be sealed, could have your birth name on it. The church goes by the cannon law of the church and is not under obligation to state laws in this regard. The Catholic church has changed it's position on baptizing all babies in it's care and no longer will perform a baptism without knowing for certain that the child will in fact be raised a Catholic. I am not sure when this change went into effect.