Should I give my promise ring back?

I’m wondering if I should give my promise ring back that my now ex-boyfriend gave me he just broke up with me tonight he didn’t ask for it back. He said I could keep it but we’re afraid that if I keep it, it’s gonna be a reminder, but I’m afraid if I give it back, he might give it to the next girl that he’s with.

Reason he broke up with me is because he feels like we don’t jive and we clash, but he basically admitted that he lied to me when I asked him if another girl was flirting with him he told me that she was and that he flirted back a few times and they’ve been talking for a little bit, but the flirting just started three days ago, but he doesn’t think that it was cheating when I told him in my book that’s emotionally cheating whether he’s never met her or not but he said that he’s not gonna pursue anything with her and he feels bad about it, but he still doesn’t wanna be with me and I don’t wanna be with him now I’m just met him when my daughter was two months old and he’s been in her life and I know she stocked him, but it still hurts.