I too had tons of painful clogs (25+). Here is what I learned...
1) Look for a tiny white "pimple" on your nipple, that corresponds to the same spot on your breast that has the clog. If you find one, it is a clogged "sprayer". Take a sterile needle and gently poke it into the SIDE of the pimple (it doesn't hurt a bit). The stuff that will come out will be the consistency of toothpaste (it's essentially dried milk). Don't be surprised if milk starts dripping out of your breast once you release the "sprayer". Then, either nurse or pump to drain the milk gland.
2) If you can't find the tiny white pimple, continue to use warm compresses. I would sometimes take a hot shower, and kind of "milk" that breast. While in the shower, take a washcloth and kind of "scrub" the nipple (which may release a tiny pimple that you couldn't spot).
Seriously, almost every time I had a clog, I had a little white pimple on my nipple. Once I knew how to recognize this, I grew much less apprehensive about getting/curing those darn clogs. Lastly, once you resolve the clog, the pain doesn't go away immediately. My boob always hurt for 25 hours or so afterwards.
Don't think you are doing anything wrong.....you're not. And neither is your baby. Clogs just happen.
Hang in there!
D. (nursed for 38 months!)