In Vafthrudnismal, Odinn competes on knowledge with the jotunn Vafthrudnir. Here, Odinn asks how Aurgelmir* was made and Vafthrudnir replies:
came drops of eitr**,
multiplied, and a jotunn was;
from here that kins
therefor we are all evil"
But, no, Aurgelmir is not the allfather of jotunn. He is the ancestor of existence.
In a note to Personified: Neither Hauksbok, Codex Regius nor any other material concerning the Norse creation myth mentions that Ymir was killed by the sons of Burr, with the exception of Snorri's Edda, a book deeply infruenced by his contemporaries. He uses the word in the chapter Gylfaginning (The Illusion of Gylfi).
*Aurgelmir is the same as Ymir.
**eitr, as most heiti in traditional norse poetry, has multiple translations. Here are some examples of a possible translation: wrath, cold, poison, curse.