I understand it as :
She was so alone (= alone to such a degree that) that I was the only one she knew, but she didn't even (at that time/in that place/in those circumstances) have me.
If that is the meaning, only "have me" makes sense. As an alternative, you might have written "... knew, but she had not even me."
All are references to the past, so you cannot use the present tense "have". You could use "have" in a past conditional construct such as "... knew, but she could not (at that time/in that place/in those circumstances) have even me.