Possibility of being pregnant if a lot of cramps and period is late?

Yes - possible: Reasons for missed/late periods: low body weight, obesity, marked weight ^ or v, over-exercise, endurance athletics, breast-feeding, ^ stress, illness, eating disorders (bulimia or anorexia), anovulatory cycle (no egg released), travel, hormone irregularities, drug use, meds (i.e., birth control) or medical problems (i.e. PCOS). #1 reason is pregnancy. Would take a home pregnancy test.