I checked DNS records of your domain:
my-acc.com. 1795 IN A 128.199.244.37
my-acc.com. 1799 IN MX 1 my-acc.com.
mail.my-acc.com. 1799 IN A 128.199.244.37
It's fine because 'my-acc.com' and 'mail.my-acc.com' point to same IP address. but it's better to point MX record of 'my-acc.com' to 'mail.my-acc.com', this is not necessary in your case.
Let's back to your original issue:
I send a mail to another email address I have (me@myotherdomain.com) and that mail box was able to receive it.
But when I hit reply, it gets bounced back mentioning "No Such User Here".
Does Postfix log any info in its log file (/var/log/mail.log) about your reply message? If yes, that means your DNS records are correct, sender server connected to correct server, and please paste full smtp log here to help troubleshoot. If no, still DNS issue.