Can a broken nose make it hard to chew food?

To the extent that taste is largely influenced by ones' sense of smell, yes. As far as the actual mechanics of chewing, if there are associated fractures of the palate or the mid-facial bones, then ones chewing could be effected. I recommend that you have a thorough evaluation with a qualified Plastic Surgeon ASAP because facial bone fractures must be fixed within 2 weeks of the date of injury or things become much more complex. Good luck!