This does sound like significant progress, Michel. The way you describe these "burning" sensations was a bit concerning at first. And I'm also not familiar with nostril "burning". However, jhana does mean "to burn" as Jhananda reminded us. And I can certainly see how the sensations could be interpreted as a burning, especially if the experience is paired with anxiety or trauma response, as I will explain.
The sweating may be an anxiety response. When I first began accessing a jhana, I believe it was my "fight or flight" or anxiety response would kick in, and I would begin to perspire. To the best of my knowledge, this has happened in the first 5-10 experiences of each stage of samadhi. But eventually I got accustomed to that level of charismatic activity, and now I only have anxiety response for intense kundalini and 4th samadhi and above (which I still have less than 5-10 experiences with.)
So my preliminary conclusion is that the sweating will go away as you grow accustomed to the increase in charismatic activity

Can you tell us what you perhaps did differently this time, or what you might attribute to the new development?
I must say that congratulations are in order, Michel

I celebrate your perseverance!