Could my foot be broken or otherwise injured?

You will have to see a doctor at some time but I doubt it is broken because you wouldn't be able to walk on it without a shooting pain in your foot, It could be bruised even if there is no discolouration. I'm not a doctor but I have dropped things on my foot many times and had a broken ankle and sprained other parts of my body. And if a doctor comments on here I would take their opinion over mine.