So annoyed

What is the age for the cry it out method? Asking because my boyfriend’s grandma is telling me to let my daughter lay there and scream until she’s choking and can barely catch her breath and I said absolutely not! She has been trying to get me to do it since my daughter was really little. I just don’t like the method and don’t want to do it especially right now when she’s only 3 months old and is choking, bright red, etc.