What is the problem that gets worse after you try to solve it?
Solution 1:
can of worms
informal. a situation that causes a lot of problems for you when you start to deal with it:
Corruption is a serious problem, but nobody has yet been willing to open up that can of worms. — Cambridge Advanced Learner’s Dictionary & Thesaurus
Solution 2:
See tar baby.
ODO
A difficult problem that is only aggravated by attempts to solve it.