Coolant loss.

What is your question?

The car is experiencing a strange coolant loss in parallel with strong overheating when the coolant tank is empty. After refilling it, the coolant tank becomes empty after three days. I have changed the radiator but the loss remains. I have checked the fan and it's working properly. The oil is not milky. I noticed that when I open the coolant tank it emits a sound as if there is some gas pressure. The "Check Engine" light got on but got back off after two days and several tentatives have to be made to start the car before the engine starts. A repair shop suspects a blown head gasket. However, since this costs a lot of money I would like to make sure if the above are the corresponding symptoms and if there's a way to verify this possibility before proceeding with this step.