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First of all, are you trying to access GoDaddy database from within PythonAnywhere? (if so, you will have to deal with GoDaddy security restrictions/rules on their database) Or are you trying to access a PythonAnywhere database from GoDaddy/somewhere else? (In which case, you would have to deal with PythonAnywhere security rules- which means that you will have to use ssh tunnelling for this use case)
In any case, if the database you need to access is only available over ssh tunnelling, check out the sshtunnel python package.
Source:stackexchange.com