I am going to assume that you have small pores since you don't get any acne besides the cysts. Cysts usually occur in people with small pores because the pore is pretty much closed so the bacteria can't escape, causing the cyst to form. My advice for this type of acne is exfoliation. And no, I don't mean the little scrubber beads... Thos only damage the skin and cause it to thin. The best type of exfoliation would be glycolic acid, alpha hydroxy acid, salicylic acid or something similar. Try to find a product (not from the drugstore) that has 1 or more of these ingredients in it to unblock the pores so the bacteria doesn't get trapped. The best bet for you would probably be alpha hydroxy. You might find a good brand by calling a salon & day spa in your area to see if they carry something like this.
For now, try putting a dab of hydrogen peroxide on your cyst to help it heal faster.