How can i heal a toothpaste burn?

Baking soda: I'm not quite sure what you mean by a burn. You may have traumatized/cut your gums while brushing and that is what's sore. You can put some baking soda on the area a couple of times during the day, just let it dissolve and that might help the area to feel better. If this happens again, try switching toothpaste. There may be something in this one that doesn't agree with you.

Refine your brushing: I am not sure what do you mean by saying toothpaste burn. It is most probably a soreness at the gum line because of excessive brushing that you developed. If you are experiencing such a discomfort of burning sensation in the soft structures in the mouth than it will need to be examined by a dentist for more specific treatment.

Change Toothpaste: This "toothpaste burn" may be the result in a response to some ingredient in the toothpaste. Try another brand and give it a week or so to heal up. If problem continues, check with a health care provider.

Warm salt water rins: Warm salt water rinse 3x day.

Toothpaste burn: Toothpaste can harm seen, sometimes to the point of leaving a scar. Toothpaste should never be used anywhere except in the mouth, just like you wouldn't use skin cream to brush your teeth. Please see a Dermatologist, a skin doctor, ASAP to help prevent permanent scarring.