I had this problem for the last year, I tried anti dandruff shampoo, showering twice a day, changing my diet, etc. and no dice. Everything I read said the problem could be fungal, bacterial or other so I decided to just try a shampoo that was both antibacterial and antifungal, within a week they spots and lumps on my head cleared up - I'm well pleased and it turned out to be pretty cheap too (£8.20 for a very concentrated bottle), it's available from Amazon in the UK:
I'd recommend trying the smaller bottle first to see if it works
I tried to find it on the Amazon in the states but it doesn't seem to be for sale, I even tried to find a substitute based on the active ingredients but no luck so I suspect they aren't allow in the U.S. or use a different name.