Yes, your Federal and State refund will come separately. The IRS states that most refunds are received within 21 days from the time a return has been accepted and a refund option is selected. The IRS will hold the refunds claiming EITC and ACTC-related returns until Mid-February and deposited no later than February 27, 2018. You can try looking it up at Where's My Refund? Sometimes it may take a little longer to show up in their system.
State refund times varies, click here for information regarding the State refund process.