You think you are not under Contract, but you have an Escrow.
You must have a Realtor representing you; but you are not communicating.
The Closing date is approaching; but you don't even realize that you have to get your Loan in place, not to mention doing your Inspections.
You should be talking to your Realtor.
They house is 100% yours for sure once you get the key and deed and give them the $. Now, it means if they did not make a mistake than yes, they will not most likely look into other offers after you get the signed/executed contract.