The lumps are probably swollen lymph nodes which mean that they are working hard to fight off the inflammation the dye has created.
Has it gotten worse since when you first dyed your hair or is it just remaining the same? You might have to take some prednisone if you can't get rid of the inflammation. Sounds like it became systemic now. Check with your doctor or even go to the ER.
I can't use dyes or a lot of shampoos because of the toxic chemicals. I've had to take prednisone when it was really bad and not going away on its own.