I Had Laser Hair Removal Last Week, and I Squeezed a Hair Out.. but It Felt As if It Was Ready to Come Out.. Did I Ruin It?

It is normal for hairs to pop out a few days after laser hair removal.  You have not done any damage.

I'm unsure what you mean by the fact that you plucked out hairs last year during treatment and "ruined everything". It doesn't. The follicle is what's affected during laser hair removal. Many people can and should experience hairs falling out within a week or so of a laser hair removal treatment. When the bulb of the follicle is destroyed, they can fall out.