Am I required to follow up with a representative after I fill my taxes out? Do I need to send something else to the tax departement or I'm good to go?

Once you e-file (or print and mail) your tax returns you are good to go.  There is no need to contact a representative.  If a few instances there are requirements to mail something to the IRS or your state, but you would have received instructions about that as you were finishing your return.