How do you know the closings are back to back (the correct term would be "concurrent") if you don't have any paperwork with a closing date?
Who is handling the closing? Title? Escrow?
IMHO if you do not know the answers to these questions, how do you know that you even are closing?
Please post more information. I agree, you need competent, professional representation.
Your attorney and agent should be able to guide you through this. Talk to them.