Thank you for the query.
From your description most likely this is sebaceus cyst
can not be squeezed and popped). It grows back because it is surrounded by keratin sac which do produces the cottage like masses. And only those masses can be drained. It helps only temporarily, however the sac still produces the masses so it grows back.
Sometimes such cyst gets infected and also puss accumulates in it so it gives pain and redness.
To permanently get rid of it, it is necessary to remove it with the sac. It needs to be done in local anesthesia
by a surgeon (or dermatologist
Hope this will help.