I happen to me around 6 weeks too and it was only on one side i swore i was going to have an ectopic pregnancy but no im 34 weeks and 5 days with a baby girl!. I heard of a few others having that too. I wouldnt stress out too much.
Yes this is very normal. The cramping you feel is just your uterus stretching and getting bigger to hold the baby as your baby is growing.