Apologizing for a joke

Hi I’m a 26M dating a 28F
should you apologize to your significant other if you made a small joke but it got interpreted way out of proportion?
Let me elaborate In the past I made a very light joke about my girlfriend insinuating that she was planning to have sex with another due to their conversation getting spicy. She did not like it and i apologize and promise to not do it again.

yesterday i was talking about my drinking habit, i usually drink some liquor at the end of the week because I’m usually stressed but not in an exaggerate way enough to get a bit drunk but not too deep. She expressed her worries and she told me I’m too young to drink. I understand that she is worried but i hated the way the said . I send her a text about it telling that i was not ok with how she expressed her worries but i forgive her because she wasn’t deliberate.
She still refuse to apologize and say she’s right.

Usually I’m very calm and introverted but i believe that if I do not talk about it now it could be way worse if she does that in front of friends.
What do you think
EDIT: i told her and she said she doesn’t see what wrong in her way of saying it . In my country it’s common to say that to friends like saying ni**a between black people . I do understand her point but i don’t want this kind of language with the person I’m interested in. We had to argue for 2 full days and then she apologized.

I’m sensing Red flag what do you think?