Will my hair grow back after dying it?

you should be seen by a hair restoration surgeon as soon as possible. you may have chemical burns from the dye, the hair may or may not grow back. There are some options that are available to you which will be discussed in a consultation with a hair restoration surgeon. He/she can examine your scalp and provide short term and long term options. 

Dying the hair and burning the scalp can be related and cause the types of symptoms you are reporting. These are chemical burns. See a good dermatologist for assistance.