Possibly a question for r/Islam, but I thought I'd ask here first.
I've read several times that Muhammed, having had his first vision/religious experience/whatever, was quite worried that he was possessed by a Djinn, but his wife (and another guy?) reasurred him that it must be indeed from the Angel Gabriel.
But, how do we know this? Is it from the Qu'ran or one of the later biographies of his life? Or a hadith? I'm very interested in understanding the events around this, and how Muhammed thought of it. But for that, I need to know how reliable this story is.
Most of the major biographical details of Muhammad's life come from the numerous sīra (biographical works) pertaining to him, which were themselves part of the same tradition of information-gathering which produced the ḥadith, the second most important source of Islamic knowledge after the Qur'an. Most of the various sīra were produced during the eighth century (many of which only survive as part of even later texts), and were based upon oral reports passed down through a chain of transmission known as a silsila, essentially a list of names indicating by what means the information passed down from the time of the Prophet until the time of the creation of its written record. The early Muslims were very careful to ensure that the sources of their information were credible, though despite this it's impossible to know how many distortions and fabrications slipped through the cracks.
That being said, when dealing with sources of this nature it's a fool's errand to attempt to gauge how "reliable" they are. The sīra and ḥadith present a certain view of the world. They give us insight into what early Muslims thought and believed about the Prophet and his actions. There's no real way to look past them at "what really happened" because they're the only sources we have for the very first years of Muslim history. So when you read the ḥadith and biographies of the Prophet Muhammad you'll learn what Muslims believed/believe. How closely that resembles the actual reality of the past, no one can truly say.
As for your particular question:
Nonetheless, all the sources agree on this basic outline of events: After his first experience of receiving the revelation, Muḥammad took three years before he began preaching publicly. During that time, he discussed these incidents with his wife, Khadīja, who helped him understand the nature of the supernatural events. All agree that she was the first to believe in his mission, though there is a significant dispute about who among the men was first: His cousin and eventual son-in-law ʿAlī, his freedman Zayd b. Hāritha, his friend Abū Bakr, or several others.
From Jonathan E. Brockopp ed. The Cambridge Companion to Muḥammad (Cambridge University Press, 2010), 6.