I figured that if you are using exchange(example poloniex) you will pay 0.0005BTC for fee and they will pay so high fee that transaction will be confirmed in first block.

It is far away from solution, and I feel your frustration.
You need to wait a little bit more, just post in here once that it gets confirmed.. But $150? Seriously? The maximum fee that you can send in order to get it confirmed in less than 30 minutes is just 0.0023
It has been confirmed, OP said that in second post. Also if you look at txID you will see why OP payed high fee.
