Sore on my feet don't heal. Could I have diabetes?

Maybe. You could, but there are a lot of possibilities that affect wound healing. Thankfully, screening for diabetes is very easy - a simple blood test can tell you if you have it. If not, your doctor can help look for other causes.
MAYBE. Diabetes could be a factor. Smoking is a BIG factor. You need to see a podiatrist to determine the reason.
Potentially. A good medical check up would probably be a good place to start.