No relationship is real without some fights. They are completely normal and even heathy, as long as you do it the right way.
Arguing can help resolve conflict, bring passion back into the relationship, and provide an outlet for repressed feelings. All this is true if you manage to include what psychologists call 'closure' to your arguments: forgive each other and move on.
If you fight more frequently than before, and for silly reasons, something is wrong. Worse, if both of you keep bringing up past mistakes, scoring points, resort to offending each other and stop communicating for days, then something is seriously wrong.
It's time to sit down and decide where this relationship is going.