Can a group of 4 teenage girls who help each other in achieving their dreams be considered an organization?

Yes, of course you can be an organization. It sounds like a great plan to be supportive of each others' ideas. Your group has a name, which is great. You can start a free website or blog and let others know what you are doing.

This is a very good question. Much of law is about deciding whether a particular action or event fits into a category. It's a little bit harder to answer your question because I don't know what the definition of an "organization" is in your particular circumstance. For example, if you are trying to get a school to allow you to meet regularly in a classroom, you might not be considered an "organization" because it sounds like you don't want to let others into the group and schools generally like groups to be open to everyone. If you want to raise money to support your group in its activities, the funders might not consider you an "organization" because you haven't established a legally-recognized business. However, a great many businesses have started in circumstances similar to yours and have grown to become nationally known "organizations."