be demiromantic asexual girl

I just recently discovered I'm asexual. I have no idea what will happen if and when I start dating. Will guys be ok not having sex? Would they say they're ok with but go behind back to other women? Will people just think I'm looking for attention? Do I need to come out? Would my parents think I'm lying. I have all of these thoughts in my head now. But I'm happy. I know who I am. I hope that I find someone someday to love me for me.