Unless you have Sound enabled to notify you when a message arrives, there does not appear to be any way to know that a message arrived for you while you are chatting with someone. Also, there is no way to tell who sent it.
Should there be an icon that appears next to the contact’s name that indicates they have a message waiting for you?
This has happened to me several times and the only way I know of to check to see who it was that sent me the message, is to check every contact.
Thanks!