Cysts and recurring infection

I got two wonderful cysts on the lower part of my jawline. They finally
both erupted and I did squeeze out all the great stuff. I even dabbed it
with isopropyl alcohol to kill any bacteria. The problem is, they keep
getting infected over and over! I try to leave them alone and they just get
kinda painful. In the past, despite what some people suggest, squeezing has
been the best way to get it over with. I even ice the area after squeezing
since sometimes that helps move it down quicker. These two are just very
stubborn and it's rather unattractive - not to mention a bit painful. Any
ideas??