I think if you start with a referral by your GP to an endocrinologist and/or a dermatologist it would be covered - subject to usual franchise and co-pay. I don't think trichologists are doctors, so the odds of being covered by insurance might not be the same as if you start with a medical doctor.
Have you recently had the full range of blood tests? I ask this as hair loss can be caused by several things. Best to rule out an underlying condition.
I lost nearly all my hair last year (head, beard, back lol) and it has now grown back as thick as before. I went through the full range of blood tests via my GP and iron was high and vit B was low. My (Syrian) barbour said not too worry it is just stress, I saw this a lot at home. If it is falling out in patches as mine did then just keep cutting short as possible with an electric shaver and wait for it to grow back. If it is falling out/thinning evenly it is probably something else and should be examined a bit more. Our GP is excellent and said there is no test to conclusively prove the cause so blood tests are the first step and supplements to get general health tiptop is the second and time is the third. The upside was a cool head in summer and no barbour's bills!
Whilst I had a reason for a full checkup not all the costs were covered by insurance (Concordia) so it pays to ask the costs upfront if this is an issue.
Thanks for your reply but this has being going slowly since years, I guess it does not hurt to have a check up through the doctor however I would prefer to reach out to a trichologist which is indeed a dermatologist, it is just very hard to find one here in Switzerland!