I wished my ex birthday but Im still hurt for what he did and didn't get proper closure, should I let it out before no contact again?

We broke up since June this year. He hurt me with harsh words in the end. He didn't even apologize and reach out to me within months. But I still love and care about him. His birthday I wished :

Happy Birthday. Wherever u are, i always pray for ur happiness & success. U still mean everything to me & i care about u. I’ll always cherish every memory we had. I hope u have a memorable birthday with ur family this year.

He replied :

Hey thank you :), normally i’d wish you success and great future, but you already have those. so i wish your health. take care.

I feel relieved of wishing but its just I still didn't get proper closure and Im still hurt with the things he said to me in the end before this. Could I let it out to let my wound heal? Maybe it would help me to feel better after letting it out although he doesn't care.

I wished my ex birthday but Im still hurt for what he did and didn't get proper closure, should I let it out before no contact again?
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