I am also using el-capitan with mail as my primary email client.
Yes you can add your dreamhost mail address to internet account what you need just the mail address, password, server address usually your mail.domain.com
I don’t have any issue to add my dreamhost mail address my os x
I advise you to use pop3 so it can clean up you mail box immediately after you check you mail you can set these in mail – preference – account — advance
you need keep you mail box clean, or else your mail box will be broken.
I am experienced it few months ago even though I have those setting, I am forgot that pop3 didn’t fetch any email in old.message folder so it end up I can not access my mail box anymore, which I think it like what happen to OP (original poster)
I think what happen to me because I am rarely to check my mail via web and didn’t check the old.message folder, but now I am learn my lessons, always keep my mailbox clean and times to times login via webmail and look for the old.message folder.