Loosening phenomenon (stitches protruding) after double-handling due to burial in July 2016

I had double eyelid surgery in July of last year.
It was buried, and I only heard that it was made with meltable thread, so I didn't untie the thread separately.

After the surgery, a small scar appeared behind the double eyelid line. I didn't think it was a big deal, but it looked like a pimple, so I squeezed it and found that it looked like hardened pus and a thread came out. At first, I didn't know it was thread, so I pulled it, wondering what kind of hair could be that long, and it went right back in. When I pulled it, it went back in again, so I cut a little bit off with scissors.

And when I looked, there were two lines of light blue thread. And right away, my eye was melted (on one side).
 I called the hospital in charge and asked about it, and they told me that the muscle-tightening thread was not a separate soluble thread. These were things I had never heard on the day of surgery. If I had known, I would have been more careful.
And does it make sense for the thread to stick out of the eye?

I'm asking this out of complete ignorance.

Can I get reoperation for free? Or, I wonder if I can receive compensation or something.