Firstly, you are not always in a lot of pain, and there isn’t always a lot of swelling with a bone break. It depends on the break and it depends on the person’s pain threshold.
I broke my wrist years ago during gymnastics, yet carried on, although it was very painful. It was only the following morning when what I assumed was just some bruising or a bad sprain, had become a swelling like a golf ball and dark bruising. I went to the hospital and it was broken.
On another occasion, I broke my wrist and had very little swelling but lots of pain. I couldn’t move it at all. It was broken.
I do have a high threshold for pain but nonetheless, you can generally tell when you have broken a bone.
The only option you have is to visit your hospital and have an xray performed. If it is not broken but causing you a lot of pain, they will strap it for you – probably with a splint until the pain/swelling eases and you are able to move it more.