STDs??? help please

I am a 21 y/o female. I started having sex at the age of 16 and have had 4 sexual partners since then (almost always used a condom). Recently I've been wanting to get tested for all STDs but my nearest clinic only tests for chlamydia, gonorrhea and HIV. If I test negative to these, could I still have other STDs without knowing it? My question is, will these tests also clear me for other STDs? I don't really understand how it works.. 
Any help would be appreciated! Thanks!