How can I make my custom packet dissector distributable?

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You can contribute your dissector to the main Wireshark codebase and have it distributed on all supported platforms by the Wireshark project for free.

As a bonus, the dissector will be maintained by the Wireshark developers and you'll get your name added to the "Authors" list.

See the wiki page on Submitting Patches for guidance on how to contribute.

I wrote the dissector in C currently. Is there any way to distribute the C dissector?

Make up a package, such as a tarball and a zip archive (provide both to support both UN*Xes and Windows - some UN*Xes may have a zip command to build a zip archive), with the source code, any additional files, and a README file telling people how to build it.

Sadly, that's the only way to distribute a dissector and make it usable on multiple platforms. Each Linux distribution might have to be treated as a separate platform - as far as I know, the only guaranteed form of binary compatibility for Linux distributions is at the system call layer, not at the shared library API layer, unlike, for example, macOS, Solaris, and Windows.

If you write your dissector as an LUA script then users can invoke it on the command-line (Linux, Windows, etc) using the -X argument. I use this myself for a few internal LUA scripts. It would then look something like:

wireshark -X lua_script:"pathToYourLuaScript"