Round ligament pain feels kind of how you described. For me it felt like a pulled or stretched muscle in my belly. It hurt worse when I strained, like changing positions in bed, sitting up from a lying position, or standing from a sitting position. Laughing, coughing, sneezing, and even bearing down to have a bm all hurt. For me it was worse on my right side, and I figured that's because I am right handed and stretched my right side more. But it was definitely on the underneath side of my belly.
Mary's right- if you're having cramps of any kind, or anything that you just feel isn't right
you're best to call your doctor, just to get hear from him that it's nothing. It's probably nothing, but wouldn't you rather hear that from your doctor than some strangers on a message board?
Good luck, and I hope you feel better!