I have never heard the term "interior conflict", but I don't want to say you can't use it. "Inner conflict" is usually something that happens within a person when that person has trouble making a decision or reconciling certain things. "Internal conflict" can be the same thing, and it can also be the conflict that happens within a group: a family, a group of friends, a sports team, a company, a government, a political party... "Internal conflict" is the term I would use most naturally, no matter whether I was talking about one person or a group.