Edited

It sounds like you have contact dermatitis, you are allergic to the shampoo you were using. I'm not a doctor, but I am glad you are going to go see a doctor. In the meantime maybe some antihistamines and/or hydrocortisone over the counter at your local store can help.

Here's a health line article about scalp dermatitis.

There's also this blog here that talks about scalp conditions.

I'm pretty sure once the allergen has been eliminated that your hair and scalp will recover. It's probably not worth buying new products yet until the doctor can look at you but if you need products that are more friendly (fragrance free) to eczema and such in the future, there is vanicream/free and clear. Sorry this is happening to you. I had dandruff before and I thought that was really bad, a medicated shampoo prescribed by my doctor was able to clear it so I am hoping your doctor can do the same for you.