I have been eating a lot of pomegranate though, could that cause constipation?

Possible: Pomegranate is a good source of fiber and usually is helpful in people who are constipated, and may help "regulate" their bm's. However, everyone metabolizes food differently, and too much of one thing can sometimes be detrimental and cause the oposite effect, inyour case, ...Too much fiber may constipate you. Find a happy medium with fluids and fiber in an attempt to regulate your stools.