Could chewing cinnamon chewing gum, cause mouth soreness or bumps?

Perhaps: You may be allergic to the cinnamon or it may just be irritating to the soft tissues of your mouth. Where are the bumps, and did they first pop up after chewing the gum? They are more likely to have been there and you merely became aware of them due to the soreness. If they do not go away within a couple of days, see your dentist for a definite diagnosis.

Gum chewing: If you have an allergic reaction to something in the gum it is possible. May not be the cinnamon, but cinnamon gum does tend to be "strong". Have your dentist check the tissue and any other possibly related issues that could cause this if it doesn't go away soon. If it happens again you may need to try another brand or flavor.

Cinnamon sensitivity: Many people are sensitive to cinnamon. Stop chewing cinnamon gum and using other cinnamon flavored foods and see if your soreness goes away in a few days. If it does not then see a dentist about your sore tongue.