Need help from a baby wearer

My 2 month old appears to be squished in the baby carrier. She has a hard time moving her head side to side. I used it when she was a newborn but now she wants to be part of the world and it annoys her. Are there baby carriers that protect the head and still let the baby move around. This is the first time I am using a carrier. I got a cheap infantino newborn carrier and don't want to shell out a lot of money for something she won't like either way.