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I want to use an ECC private key for encryption because of mutual authentication.
But I cannot find a method (or function) in wolfcrypt (wolfSSL) or the micro-ecc library.

Is is okay to use an (ECC) private key for encryption?
And if so, how can I do this?

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No. In Public key Infrastructure(RSA, ECC) the private key is used to decrypt and the public to encrypt.

Furthermore, you can use private key to sign with digital signature. And the Public key to verify the integrity of the signature.

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