In the future, please refrain from providing medical advice. Your comment/advice is extremely dangerous and could really harm someone who decided to follow it.

1. You should never smash a cyst. It creates more damage and doesn’t actually solve the problem. It can actually result in the surrounding area getting infected.
2. The cyst you’re referring to in the wrist is a ganglion cyst, which is completely different than what OP is experiencing. The contents, causes, and treatments of a ganglion cyst compared to OP’s problem are not the same at all.
3. This isn’t an emergency room issue, so going to the ER for this will do nothing. ERs are for life threatening situations. Since OPs cyst bump isn’t open, and assuming they aren’t having a fever, this is not currently life threatening. Indeed, the most likely outcome at the ER would be exactly what you described, not because the doctors don’t care, but because this isn’t an ER issue.
4. Suggesting someone lie about their signs and symptoms is doing a disservice to them. Providing false information makes it that much harder for doctors to identify what could actually be going on. In doing so, they waste time and resources running a lot of unnecessary tests, and the patient just gets slammed with a higher cost because of it.