I know, but it may help others.
I have this same issue and it makes my laptop virtually unusable. I made an account to see if o could get a solution.
Sorry to hear. 
As far as the problem goes:
After trying out several Live installations (Manjaro KDE, Gnome & Ubuntu) I’ve contacted the Lenovo support since I’m starting to think this could be a hardware issue. Besides advising me to install Windows and see if the problem occurs there as well, they told me I should see if this is also happening in the bios. I’ve tried that and although it’s hard to tell because you cannot select or move anything, the touchpad seems perfectly usable there. Therefore I would say this is not a hardware issue, don’t you think? 
Can you try out how the touchpad is behaving in the bios @Beanpe?
I just came across your thread as I am having a similar issue, though my issue deals more with the jumpy/jittery cursor as opposed to clicking. I have had some clicking pressure issues, though. With that said, I can confirm that the issue does not occur with Windows. I have had this laptop (Lenovo X220t) since it left the factory (c. 2012) with Windows pre-installed and there were no problems. I later replaced the HDD with an SSD and put Linux on it. I have run numerous distros based on Debian, Arch, and OpenSUSE, and all have had the same problem. It seems to me to be some sort of driver issue, but I cannot be certain.
I know this is not helpful in the least, but I did want to confirm for you that the touchpad works fine with Windows.