Easy fix:
for(var i = 0; i<my_dg2.dataProvider.length; i++){
if(my_dg.getItemAt(i).firstName == my_dg2.selectedItem.firstName){
trace("match found!");
}else{
trace("no match found. :(");
}
}
It searches your whole datagrid for matching text. That code is not completely accurate, but should give you a lot of headway into your problem. Hope I helped. 
