A one way hashing function can only be use for the integrity of a message and not for authentication or confidentiality. Because the hash creates just a fingerprint of the message which cannot be reversed and it is also very difficult to create a second message with the same hash.
A hash by itself does not provide Authentication. It only provides a weak form or integrity. It would be possible for an attacker to perform a Man-In-The-Middle attack where both the hash and the digest could be changed without the receiver knowing it.
A hash combined with your session key will produce a Message Authentication Code (MAC) which will provide you with both authentication of the source and integrity. It is sometimes referred to as a Keyed Hash. A hash encrypted with the sender private key produce a Digital Signature which provide authentication, but not the hash by itself. Hashing functions by themselves such as MD5, SHA1, SHA2, SHA-3 does not provide authentication.
Source: HARRIS, Shon, All-In-One CISSP Certification Exam Guide, McGraw-Hill/Osborne, 2001, Page 548