Somewhat large-sized filling fell out of a (bottom) tooth a few days ago. yesterday i started having a sore throat. could these be related?

Filling: yes if its on the same side as there is a nerve called the trigeminal that would provide sensation to those areas. Check it out to make sure its not a bacterial throat infection

Maybe: Your pain may be related to the tooth or it may be a virus or something else. The only thing for certain is that it will take a dentist to treat the tooth with the lost filling. See a dentist ASAP and get the tooth treated. It will only get worse the longer you wait.