Missed period

Hi, I am 24 yrs old. Have had unprotected sex but as much as I an my partner remember it was a very quick one and nothing went inside. But, my period is late by 15 days and no signs of it coming either. I did a home pregnancy test which came negative. Do you think I still could have conceived? Also, is aborting a first child a good thing to do will I get problems in my pregnancy later. I am unmarried an can't let my family know of this. Pls help!!