What type of shampoo are you using? When you say your scalp is burning do you mean it burns when you get a relaxer or do you get a burning sensation randomly? Is your hair relaxed or natural?
Again, there could be several reasons for what you are describing. If you relax your hair then you could just have a sensitivity to the chemicals. Relaxers can leave a burning sensation for days after the service. If this is the case then you should make sure that your stylist bases your entire scalp before every relaxer service for your comfort and make sure they rinse the product out of the hair properly with warm water and good water pressure. Any product left on the scalp will continue to work and can cause burns and scarring. Also, make sure they are using a quality no-lye relaxer as these are gentler on the scalp.
If your hair is natural and you shampoo it daily then it could be an allergic reaction to the shampoo you are using. This could also be the cause of the red spots. You should use a good moisturising, sulfate-free shampoo that is gentle and doesn’t strip the hair and scalp of it’s natural oils.