If you are feel happy when you identify as a girl, then you are a girl. Some trans people never have surgery if it's not for them, and frankly, its no one's business if you decided to transition through surgery or not.
Just because you can't afford surgery or just don't want to do it doesn't mean you can't be a girl. If wearing feminine clothing would help you feel more comfortable you can always go out and purchase some, and if money is an issue, there are tons of communities online where trans males can trade clothing with trans females for free!
There are also other resources for trans females that provides fake padding for your chest, and other stuff that can make you feel more confident your body. However, if your suffering from gender dysphoria, these methods may not help.
If you strongly feel that you need surgery in order to be happy, then definitely do some research on it and reach out to LGBTQ communities on the web to see if it's the right choice for you! If you ever need some more resources or info, feel free to DM me! Good luck!