Try posting your question on the X10 tech support forum - Free Hosting.
That forum will be able to help with your individual DNS issue.
Tech support at register.com may also be able to help if you care to ask them.
I have no knowledge about register.com only how the Internet DNS works.
AFAIK, what you are trying to do can only be done by directing your DNS service for the free mydomain.com name to X10Hosting's nameservers at register.com and then creating a sub-domain irc.mydomain.com on your free X10Hosting account via the cPanel.
You can use your free mydomain.com name at X10Hosting by using the Addon Domain feature in cPanel, then you may create the irc.mydomain.com sub-domain using the cPanel feature once again.
Do a search of the forum for addon or parking or DNS etc to see if there is any posts that may help you to understand how hosting and the DNS at X10Hosting works.
I can't help you any more on this issue as I have no knowledge of what arrangements you have with register.com - if you are meant to host your free mydomain.com at the place you acquired the free domain from, then you will not be able to host that mydomain.com at X10Hosting because you will not be able to transfer the DNS service to X10Hosting.
Regards,
Rocky