I am a diabetic and have a purple bruise that is sore in my belly button?

I assume you don't inject medication there. Minor trauma to the navel that you weren't aware of has most likely caused the soreness and bruise. Spreading redness would be concerning for cellulitis, which requires antibiotic treatment. See your physician as needed.

It is impossible to tell from just this question what is the cause of your sore. It would be more appropriate to see your primary care doctor, or set up a health tap consultation with good pictures of the soreness, as an initial step in the workup. If the purple bruise persists, do not hesitate to get it examined.