Ok, update here.
I did everything you suggested. I completely restored my iPhone to factory settings, then I moved in my data partially and manually (not through an iTunes backup). After that I even calibrated the battery with the process suggested by someone here.
The first week or so everything went amazing. The difference in battery performance was incredibly differentand I event thought the problem was software-related and definitely solved. However, after that period of time, things starting to get weird again.
I could tell you how bad the performance was, but I prefer you to see it by yourself. In the attached images (it's only three pics, don't be scared) you have a detailed view on how damn fast the battery was draining during one of the previous days. Please check the battery percentage and the clock, so you have a more accurate idea.
I don't know if I had the opportunity to snap it in those screenshots (they just cover the upper 50% of battery-draining), but at times I could see the battery going down 1% in 10 minutes, and sometimes in just 2 or even seconds (which is why, as a matter of fact, there are some percentages missing in those screenshots, because I wasn't fast enough to go the settings and take a screenshot).
I don't know what to think now. Do you still think there is something weird in the software, or definitely it looks like a hardware issue?
One would tend to think about the latter, but that doesn't explain why everything went so smooth during the first 1 or 2 weeks.
Hopefully you can provide me some guidance, because I really need my phone to work properly

.
Thanks in advance!