The Seeking Thing by Janet Hirsch

This story came to us bearing a masculine-sounding pseudonym, but inquiry revealed that the author is, as she puts it, "the suburban Mother and Wife. I do some real estate advertising and spend much of my time traveling the Long Island scene choreographing two or three musical shows each year."
Let us state for the benefit of all that in this office no female horror author will be overlooked, as our newcomer feared. This might have been a danger thirty or more years ago, but not now, when one cannot make even a cursory list of top horror writers without encountering the deadlier-than-male. No reflection of course.

The second short story of the issue 'Magazine of Horror, February 1964'.