-Have your new employer filed I-129 to transfer your TN and got approved by USCIS yet? If yes, that means your status is OK and you just go to work for the new employer (if your status has a problem, USCIS will deny the I-129).
If the new employer has not filed I-129, you need to go to the US-Canada border to get the new TN I-94. Don't see you will have a problem to get the I-94 in this case. So, not need to be panic.