Your own hits on your webpage should not be counted as unique visitors after the first time.  There is supposed to be a cookie set by Flagcounter that should mark you as a previous visitor so that your unique visitor count is not affected by your own visits.  Obviously page-views will still go up based on your visits because whenever you load up your web page, it is technically a page-view.

I don't think there is anyway to manually adjust the stats on flagcounter, so you can't selectively uncount some of the hits.  You either have to live with what the counts are, or you can get rid of the current counter and generate a brand-new one (and the counts would start from zero).