4 Month Old has throws horrible fits

My 4 month old daughter has started throwing some pretty horrible fits and I was just wondering if this is normal. This is my first child, but I have been around many small babies and have never seen any of them have such horrible tempers. It stated out just around nap time or bedtime. Its not even that she is crying, she is just literally screaming. She stiffens her whole body, and her face turns red, and she starts pinching whatever she can grab or pushes me away. She will sometimes scream like this for 20 minutes. I have tried letting her cry herself to sleep but after half an hour she is still just screaming. She has now started the fits when I try to let her sit in her swing or play on her mat in the floor, and it can be right after a nap even. So its not just when she is tired. I was just wondering if this is normal behavior or if it is something I should talk to her doctor about?