Question about use of IV in this cipher
Different modes of operation have different requirements. For example, the IV for CBC mode should be generated with a CSPRNG, where as the IV for CTR mode just needs to be unique for each encryption.  In terms of cryptography, the 'random' functions found in many languages are more predictable than you might imagine.

That being said, there's absolutely no need to encrypt your IV.  It doesn't need to be secret, and can be transmitted/stored as clear text.

Encrypting the IV might add some level of security, but if you plan to do that then you should use a key which is independent of the key used for the initial encryption.  Independent not only means unique, it also means that it's derived from a different source (which can make things unnecessarily complicated).