I have installed windows 10 on my computer a month ago and it worked well
At any point in time during that month did you perform a disk image backup of your drive, or at least backup all your critical data.
Does the computer have a factory partition from which you can recover the system to a factory state. Many computer manufacturer's include this feature / option when the computer goes out the door.
I assume that you also tried a Startup Repair also?
I'm very sorry, but at this point I do not see a lot of options.
If it was mine and I was stuck where you are now, I would backup my data (no I wouldn't because I would already have a backup and a disk image) and then I would boot from the installation media.
Press Shift F10 at the language screen and use Diskpart to clean the drive and then perform a clean custom install.
If your computer has been running Windows 10 for a month then performing a clean install should not be a problem.
Just make sure you do not make any attempt to enter a product key during the install choose "skip" and or "do this later" each time you are prompted.
Does my HDD bugged or broken ?
I have no way of knowing. Do you have any reason to suspect that the drive itself may either be failing or faulty? Was the computer exhibiting any symptoms prior to your performing the upgrade?
Can you remove it, attach it to another system and then run chkdsk against it to see?
EDIT: One last thing you might try. Reboot your system and use whatever key combination will get you into the System Setup Utility (BIOS).
Change your disk controller mode from RAID to SATA AHCI or SATA IDE or NATIVE IDE and see if that makes any difference.