Is it permissible to count the amounts paid to family and relatives as assistance from Zakat al-Mal, given that I do not remember whether I paid it in full, or less, or more, and I wish to clear my conscience now?

What was paid from zakat (definition) to relatives is not counted unless it was given with the intention of zakat at the time of payment, and provided that they are among those who are eligible for it due to poverty or destitution, and that their expenses are not obligatory on the zakat payer to meet their needs. If these conditions are met, then the total obligatory and disbursed zakat should be reviewed, and whatever remains must be given out.