Now that this is the case, you don't have to worry about whether what you did at that time was right or wrong. Generally, it is okay to sign a labor contract. No one will come back to check on you again, but you should be mentally prepared. Once the matter is exposed before you sign the labor contract, you should fully bear the responsibility for breach of contract.
Don't give yourself too much pressure. Many people have makeup or exaggeration in their resumes, so don't worry too much.
Good luck ~