Hosting provider is GoDaddy.
The guy I spoke to insisted that my website is Wordpress, despite the screenshots I sent him clearly showing a Joomla backend. So I'm really not sure how much help these guys are really going to be.

I really do not know how to react to this Samantha...
It is a value in a php.ini file, but depending on the setup, it could be located in various places and you might not have access to it.

You can take a screenshot of the error and explicitly ask to increase the Maximum execution time to 60seconds.