Am I overreacting??

I work at dollar general, Which is in a area where there are many black people, I (18,f,Hispanic) say “Good afternoon” to this older black lady who is maybe around her 60’s. Before even saying anything back to me or even looking up at me, she goes, “you sound black, now are you black?” She then proceeds to look up at me and says “nope, you are not” followed along with a sigh and continues to hand me her items. Of course I get offended by this and refuse service to her because this is not the only race-related situation I’ve experienced while working here so ofc enough is enough. She then tries to apologize and says if I can just scan her items so she can go. I refuse again and my manager comes up to the counter after hearing the commotion. Then lady tells my manager I was being rude to her for no reason and today I was just “extra tender”, fyi I never seen this lady ever. My manger basically tells me to shut up after I was trying to tell her what happened and told the lady that “different people are going to find different things offensive”, the whole time she was talking to her kind of sounded like she was taking her side for it. My manager is also black if that helps. I’m not sure if I’m overreacting for refusing her service but the fact that race even has to be brought into anything where it has no business being brought into kind of ticks me off since Im only trying to make money to pay my bills.