TN Visa Approved...Still Not Working?

[curiousGeorge]

Is there a way that I can change my status from TN to H4 while staying in the US or I have to go back at the border?

In order to file a "Change of Status" from within the US, you must be in legal status to begin with, otherwise, you wouldn't be "changing" your status, you would be "obtaining" a status. Since, technically speaking, you are currently out of status, there is no status available for you to "change from", so you need to obtain a new status.

You're much better off filing at the border and obtaining a new status, in this case, an H4.