You may have a cyst on your ovaries which may be causing the pain. I had one on one of my ovaries in my first trimester which is totally normal. Mine did not get very big so it never really caused me any pain but every person is different. I would mention it to your doctor because they may want to do an ultrasound to rule out a cyst or even an ectopic pregnancy. I had 3 ultrasounds done in my first trimester to watch the growth of my cyst. If you are talking about cramping like with your period then that is normal as long as it doesn't get too severe. It's just from your uterus growing. Either way just call your OB to let them know what is going on. Good luck.
If it is on one side only then yes it can be normal. Sometimes when your ovary releases an egg it forms what is called a corpus luteum cyst on the follicle that released it. Depending on the size of it, it can be painful...causing a sharp shooting pain or even a tugging/pulling sensation on that side. All of this is normal and the cyst almost always resolves itself by the end of the first trimester and is nothing to worry about. You may not have one with every pregnancy or you may not have felt it with your last. I am on my 8th pregnancy and had one that caused pain for the first time with this pregnancy.