Can you fracture wrist without knowing?

I slipped and fell on my back and wrist 2 days ago.
My back has visible bruising but strangely I have no pain on the bruise I have mild pain further up though sometimes.
My wrist felt fine right after and yesterday until in the evening it felt sore after I had ironed and then its gotten worse. I am wearing a wrist supporter I had at home now which helps but as soon as I take it off theres pain in my thumb-joint all the way up to my elbow. Ive sprained my wrist a few times years ago so I think the pain is similar. I have no bruising though no swelling or anything. Im thinking about if I should go to the hospital. Only my dad could drive me though and we arent exactly close so everytime I need to go to the dr for something he gets pissed and tells me I am crazy and imagine things and need to get taken to a psychward and when the dr tells me whats wrong he gets annoyed if I actually needed treatment because its like he wants everyone to be as miserable as him all the time he even wanted me to take antidepressants like him. So yeah.
And I wonder if its worth that whole ordeal. I cant go see my regular doctor because as usual the waiting line would be at least 1 week long and only the hospital has xray