It depends on your growth rate. Usually it's about .5 inches per month (of curly growth), which means, depending on how long you want it, you have to do the math and wait.
My mother was actually relatively supportive of my hair (though I never wore it down, like ever), so I'm sorry to hear that. I transitioned for around 3 years, and never truly did a BC. My hair is currently SL curly dry (BSL wet).
I also understand what you mean by differentiating your hair. I still have the random wavy/3a strands on my hair that I thought were relaxed, but I suppose they're natural. Usually, you can tell because the relaxed part usually manifests as stringy strands coming out from curls (though, in your case, your curls probably aren't defined yet). The curl pattern should be different too, but I thought that was fairly obvious. Look at your roots for the curl pattern.