A white blister or pimple-like bump has appeared on my gum.

It is most likely a fistula - a channel through which pus from inflammation at the root tip drains into the gum. While the pus is draining the pain eases and it can feel as though the problem has resolved, but the inflammation inside is still progressing. Popping it with your fingers or a needle does not remove the cause, so it fills again within days; the definitive treatment is root canal treatment of the tooth responsible (retreatment if that tooth has already had root canal treatment). Come in without delay in particular if 1) the blister repeatedly disappears and returns, 2) tapping the tooth makes it resonate, or 3) you taste something bitter or like pus.