Is is possible to fall on you hip and feel mild pain and then days later feel almost unbearable pain. Could I have broken something?

Yes to both Q's. -- See your pcp or an preferably an orthopod to get xrays +/- a ct scan maybe necessary to establish a dx, so treatment could be started. In the meanwhile take some pain meds and use crutches/walker with no weight through the affected side, till you are seen and tested.