I think it's worth focusing on the specifics of your actions here, as gleaned from your Facebook post. Apparently you went swimming in cold water, then entered a sauna, and the following happened:
After I entered the sauna room, the people there thought that I was in trouble and called an ambulance. They saw I was shaking and they thought I was talking nonsense, but actually I was only shaking very little (i.e. controllable), basically nothing when compared to what happened to me a few days before, and maybe because I don't speak Finnish so they thought I was talking nonsense.
I planned to stay in the sauna until I stop shivering at all. When I was removed from the sauna, I started shivering more vigorously immediately, and you know, the end result of that would be the hospital. ...
At the moment I was going to be discharged [from hospital] I asked what was my temperature when I was removed from the sauna, and it was 35.1°C.
So, essentially: you made yourself borderline hypothermic (35°C is the usual limit for hypothermia, and you had had some time to warm up by the time the medics took your temperature). You then entered a sauna visibly shivering and unable to communicate. Understandably, someone called an ambulance for you. Note that confusion, memory loss, and slurred speech are well-attested symptoms of hypothermia: even if it seems subjectively to you that you were acting normally when you entered the sauna, others may have noticed unusual aspects of your behaviour that weren't apparent to you at the time, or that you were unable to recall afterwards. This outdoors.se answer from ShemSeger is particularly informative on the topic (emphasis mine):
I've been in the early stages of hypothermia before, and I can tell you from experience that when you're in the early stages of hypothermia, you're convinced you're okay and that nothing is wrong; as in shivering and shaking uncontrollably while trying to convince the people around you, "Oh I'm fine, I don't feel cold at all I don't know why I'm shaking so much..." ... Once you get into the beginning stages of hypothermia, your chances of self-diagnosing its onset are slim, and it would be foolish to be arrogant enough to suppose you could have the capacity to recognize when you were hypothermic.
Does that sound familiar? Do you think that perhaps the paramedics who decided you needed hospital treatment were in a better position to assess your state than you yourself were?
Now, to your actual question:
Actually what is the proper way to use a Finnish sauna? Does it really mix with swimming?
There is no single and precise "proper way" to use a Finnish sauna, but it is often combined with swimming or a cold dip or shower. However, in several decades of sauna use in Finland and around the world, I have never seen anyone cool themselves off to the extent where they are starting to display symptoms of hypothermia. Like your own sauna companions and the other cold-water swimmers in your Facebook group, I would become concerned for the health and wellbeing of anyone who did that.