It is possible to be allergic to anything. A toothpaste allergy is something that may not occur to you until your gums are sore and you can't figure out why.
Besides gum soreness, toothpaste allergies can make the gum tissue red, swollen and cause sloughing (peeling) of the gum or cheek tissues.
Though less common, I have even heard of toothpaste making teeth feel achy and sensitive.
It can be difficult to pinpoint any allergy but paying attention to a few details will help...
Are you using a new product?
Did you just buy a new tube of your usual toothpaste? The ingredients may have changed.
Is your toothbrush new? Sometimes a brand new toothbrush especially if it does not have soft bristles, can irritate your gums.
Did you just start flossing? Flossing can make the gums swollen and tender the first time or two.
Did you eat something that may have irritated your mouth? Certain foods can cause trauma to the gum tissue, tongue or roof of the mouth. Foods with a rough texture, high acidity, or very hot foods will injure gum and cheek tissue.
Are you using any other product such as dental floss, mouthwash, or chewing gum? Any product that you may have just started using or may have over-used could be the cause.
Is your mouth dry? If you have a cold or sinus congestion your mouth may be dry. Dry mouth irritates the gum tissues. Click here for more about dry mouth.
If you have injured your mouth in some way, it should improve each day.
Gum tissue that is irritated or traumatized should be allowed to heal. Brush and floss these areas very gently or just leave them alone for a day or two until they feel better.
For symptoms that don't improve, try changing products or use them less frequently to see if the problem improves.
Any irritation that doesn't resolve or at least improve after a week is probably not the result of a toothpaste allergy and should be checked by your dentist or physician.