Your mom is lying to you, they can't tell if you have had sex, unless you were pregnant. If your mom is against you having sex, just make sure you use protection (planned parenthood)and understand that if you hymen is not together it does NOT mean you had sex.
Some parents will run off that if your hymen is gone your nto a virgin what alot of people don't understand is that you can loose it to daily acitivities. Those activities consist of biking, walking, sports etc etc...
At 16 there is also patient/dr confidentiality well there is here so your mom wouldn't find out anything but I still suggest you find this info out. Whether calling planned parenhood or your local drs office, you can find out your laws to privacy!