Female birds actually squawk a lot. Almost like they are in an argument. If you would like a singing bird, you have better odds with a male. If you want to get rid of your bird, many pet stores will take rescues are a local pound. She may be less annoying if she isn't lonely. Maybe a companion bird, but it is a risk. You may get another squawker. : )
Please don't just let the bird go. Take it to the animal shelter or put a free ad in a local paper if you want to get rid of it. Birds are just loud at times and they want to be with there family. If you can't dedicate the time to them then think about giving them up.