What the benefit of the shared key that generated from ECDH key exchange protocol? Can I use it to encrypt the message or encrypt the public key of asymmetric encryption?
In principle your could use the derived secret for encryption. But this has several disadvantages. It may leak information about the involved keys and is vulnerable by man-in-the-middle attacks.
A common scheme is to use the derived shared secret to seed a key derivation function to derive stronger keys and get better security properties (forward secrecy, ...)