I agree with arbiton.
You haven't said what you are getting for €600 but some of this money will be to pay for things that a GP can do for €65.
All GPs can get blood tests tested for free in a public hospital (as long as we are not recovering from a cyberattack).
Also, you will be steered towards using the private hospital for everything, and your health insurance may not pay for it all.
Once anything shows up, you will be directed to a consultant in the private hospital, even if is something that your GP can manage.
It is important to manage your health once you are in your 40s, but a visit to your GP and making sure to check for lumps is my advice.