Is it possible?

So I have the nexplanon arm implant & I haven't had my period in 166 days. A little less than a month ago i had sex with my boyfriend and we 100% did Not used protection... lately i been feeling extra hungry and a tad naseous here and there yet i did have a cold & heavy allergies which you know makes you have alot of flems = throw up..... sooo um do you all think i should still take a test? Is it even possible to get pregnant even if im not getting my period = not ovulating????.-.