On my guitar (Framus panthera supreme) the strings are going out of tune over time.
However, the strange thing is that instead of getting looser they are getting more tense. After I tune the guitar again a week later I have the same issue. I also noticed that the guitar has a buzz when I play on the low frets on every string (an issue I didn't have a month ago).
All this seems strange to me since it has a fixed bridge.
My suspicion is that the problem is in the guitar neck.

I would appreciate any advice on how should I deal with this.
It could be due to the weather. There is no moisture in the air where I live (wake up w/ a nose bleed each morning) and my neck has shifted some.