Can an ear infection cause an upset tummy?

I would be more inclined to suspect his medication is causing his upset tummy rather than the actual infection.  Ask your vet.  Maybe there is an alternative med.

I would think just not feeling well in general he would not want to eat... just like humans. Or maybe the meds are causing some gastro problems and that is causing loss of appetite.

When you say ear "infection" are you saying yeast or bacteria??
 
Most 'drops' tend to be for yeast (and that's a sweeping statement and obviously I haven't a clue what your vet gave you).  But if it's for JUST yeast, I would get the dog back to the vet ASAP.  Because my suspicion is that it's bacterial and it's DEEP. 
 
IF (if if if if if) it is bacterial then the eustacian tubes could well be infected and the eustacian tubes lead from the ears to the throat (when you swallow and make your ears 'pop' you are forcing air thru the eustacian tubes).  IF it's a bacterial infection that is serious, it sure could make him sick to his stomach if the system goes septic generally too. 
 
Head shaking typically is "yeast". BUT BUT BUT very often the underlying bacterial infection goes undetected.  The vet may ultimately need to do a culture and sensitivity test (pricey but ASK FOR IT).  That will culture the yuck deep in the ears and will tell you exactly what bacteria it is and what will treat it.  But I'd think it's a really good possibility it's deeper than the vet suspected.  Often bacterial infections can go untreated and they can be VERY serious.

Thanks for the replies.  Mac is doing much better and is acting like his old self.  He has his appetite back and is pooping normally so I think the diarrhea was unrelated to his ear infection.  Callie, to answer your question, yes, it was a yeast infection.  I appreciate the info about bacterial infections, it's definitely good to be aware of.