Search Results: best way to break-up

So I and this girl have been talking for almost two and half months, everything was great at the start and then suddenly out of nowhere she told me that she did not like my name calling or swearing at her as it showed her I didn't respect her and I had hurt her. Initially, I could believe what she said because I was so oblivious to it because of that's how I talk to my best-friends and previous ex (Bare in mind I swear a lot I don't know why) and it was never my intention to hurt her. Anyway, I complied and stopped immediately swearing or any name calling because it would hurt her and that is not what I want to do to someone that I care about.

Fast forward to now, yesterday I basically said it's over because she actually has sworn/name-called at me more than FIVE TIMES ( I have not sworn once at her after she told me to stop). I told her more than three times previously that it is unfair for her to call me names but not there another way round and I won't stand to be DISRESPECTED like that ever again. Every time I told her that she keeps saying "sorry I won't do it again, I promise blah blah blah".

After the breakup text, she replied with sorry I didn't realize it was that serious to you and realized it too late and give us another chance blah blah blah tbh her apology did seem sincere to me.

However, I'm not sure if I'm overreacting because I would let my previous exs-call me names and id call them names because I always thought it was jokes and laughter, and personally was never a problem in my previous relationship. I am so angry at what makes her think that she can swear at me when she is the one who said no swearing and also she does not take my inquiries seriously because if she had then she would've stopped immediately hence showing she does not care about how I feel.

Give me some suggestions people, should I take her back or not?

Me and my ex haven't talked in about 15 days, the break up was really bad on both of us, she cried when she broke up with me. I acted terrible during the breakup and said some really bad stuff and did some messed up things. I texted her two days ago, apoligising for how I acted and hoping she doing well. She quickly replied with "Thank you" and then about 7 hours later she said "I just want to say I really appricaite that, and I'm sorry the way things ended, and how bad things got"
I'm still moving on regardless if she comes back or not, I did a lot of "Loving myself" and feel like I am almost healed. The break actually benefited me those most really..
But of course I would like to see her come back,. So between these two options what do you think is the most likely? From any perspective.

So now I ask you! Please use the best of your knowledge thanks :)