Try using a bigger piece of cotton for starters. Small cotton gets clogged faster and prevents solution from being drawn up sooner than a larger cotton will.
How much water are you using? The less water you use, the more likely it is that your cotton will get clogged. Try using between 40 and 70 units. That's a perfect amount, in my opinion.
Also, make sure the flat, beveled edge on the tip of the needle is facing down. If you don't know what this is, just look closely at the tip of the needle and you will see the flat edge where the hole is. This must be pressed flat against the cotton, but also, you don't want to press too hard into the cotton; just rest the needle lightly on top of the cotton.
It sounds like whoever you are getting your H from is cutting the shit out of it, and probably using some kind of cut that is clumping when wet and seriously clogging the cotton. Just try the things I've stated and it should help.