Logon to your Edison from a terminal as root and use this command to see what packages are installed:
Run this command to see what packages are available:
... to see what modules on PyPi exist with the characters MYSQLDB in them... (google is our friend, but even google does not have crystal balls.. )
So some research, and if you still have questions, feel free to ask.
Also, in the AlexT's repo there is libmysqld18, which contains the development header files and libraries for developing applications that embed the MariaDB. Why don't you try it, I believe it might work for you. You can learn how to set up your Edison to download packages from the AlexT's repo here: Edison Package Repo Configuration Instructions