In asymmetric encryption Both the sender and receiver have a private key and a shared private key?

No, both sender and receiver have a private key and a public key. It works like this: if you encrypt something with one key, you need the other to decrypt it. You give everyone a copy of your public key. When they want to send you something encrypted, they use your public key to send it. Only your private key can decrypt it, so no one else can read it. You don't give out your private key.