Blister in mouth with pus caused by pulpitis infection. How did I get it?

Decay/Trauma. Tooth has abcessed from what you have said. That can be after decay has progressed to the pulp or after (usually long after) trauma has caused the pulp to die and in some cases it just happens. Make sure to get it taken care of with antibiotics and further dental treatment.
Spreading infection. The infection spread through the root into the bone and after a long period of time has destroyed enough bone to start draining into the mouth.