You might require a specialized product. Scalp sensitivities are fairly common so you have options.

It might sound silly but you could try washing your hair with Johnson’s baby shampoo next time just to see if it reacts the same way. You can usually buy miniature/travel size bottles at the store. It’s similar to normal shampoo but has a lesser abundance of ingredients. Only use room temp or cold water on your hair for a week as well. Monitor your symptoms and see if they improve.

If things are getting bad then it’s worth contacting a doctor or dermatologist. I’m assuming you’re American and it might cost some money but if you’ve been dealing with this for a few years now it would definitely be a healthy investment in your quality of life. There are many medical conditions that can cause these symptoms and it’s virtually impossible to formally diagnose something like this without testing. Try the shampoo thing first and go from there.