If you aren't satsified with your dentist and his treatment of your situation, you should discuss with him your concerns. If you still aren't happy, you can always seek a second opinion from another doctor.
I would be concerned about the constant presence of blood and pus in the area. I would recommend seeing an endodontist for a second opinion if possible.
The dentist that did my root canal and my current dentist are different and they are both in Taiwan
My current dentist cut the gum open and tried to scrape away the infected area once
but the pus and blood are still coming out (This problem has been there for years)
He suggested that I squeeze the pus and blood out whenever I can feel it accumulating in my gum; however, once he did suggest that I should maybe have a surgery to remove the whole area (tooth plus gum)
What did your dentist say about the findings and what were his recommendations?
If there's pus and blood coming out, it definitely indicates an infection of some sort. You will need to find out what is causing the infection (seems like its the root canal) and depending on the extent of infection, you may need to have the root canal redone or perhaps surgery to fix the root tip in the bone. If the damage is too extensive, they may need to extract the tooth.
If the problem is caused by the root canal, an endodontist would be the proper referral. If there's a root tip left in your gums from a previous extraction and that's causing the problem, then an oral surgeon can remove that tip. Ask your dentist for a proper referral.