We can't tell you if it is broken or not. What I can tell you if it is broken, they would do the exact same thing you are doing. So the only thing getting an x-ray will accomplish is you will have a medical bill on top of what you are doing.
A few days ago, I smashed my finger in an iron door! My finger was bruising,numb,and it was swollen.My aunt got me some ice and a splint but she wont take me to get it x-rayed. It hurts so bad and it keeps throbbing. Is it broken?
If it still bothers u in a few more days, ask again.
Stop whinging. Go see a doctor.