If you received dispensations from your local bishop to marry a non-Catholic in a non-Catholic ritual, your marriage is recognized as valid by the Catholic Church. If your husband is baptized, the marriage will be presumed sacramental. If you did not receive those dispensations, your marriage will be presumed invalid. As a valid marriage is a prerequisite for a married person to licitly receive Communion, you should not receive Communion if your marriage is not recognized as valid by the Catholic Church.
If your marriage is recognized as valid by the Church, there is no need to have it blessed in the Catholic Church, although you may do so if you wish. (You cannot “remarry” but you can have your marriage blessed.) If your marriage is not recognized, and assuming that there are no obvious impediments to the marriage (e.g., previous marriage, close blood relationship), your marriage can be convalidated in the Catholic Church. Ask the staff of your local Catholic parish for help in completing the procedure. Once the marriage is convalidated, your marriage will be presumed valid (sacramental, if your husband is baptized).
