Baking soda is a very popular folk remedy for burns. It probably works by drawing some of the heat out of the burn (when baking soda dissolves in water, the result is a "cooling" sensation on the skin). However, the ability of baking soda to relieve the discomfort of the burn for any significant period of time is pretty minimal.
In any case, burns should be evaluated by a doctor
. This is to make sure that the depth of the burn is not too great, which could require more aggressive treatment. It is also to help remove any dead tissue that might impair healing. Placing a paste of baking soda, or anything else really, on the burn prior to showing it to the doctor just makes it harder to make this initial assessment.
If you can get in to your primary care doctor
right away, then that would be a good place to start for an assessment. If not, then you can go to an emergency room for a more immediate evaluation.
After the doctor takes a look, they will recommend to you what you should do in terms both of wound care
and also medications to relieve the pain.