Are both sentences Ok and natural?
I was the only one she had until she died.
I was the only one with her until she died.

Question

Answer

== American English ==

They are both grammatically correct and also natural sounding. Good job. :)

You can also write these as the following in American English:

1. I was the only one that / who she had until she died.
2. I was the only one that / who was with her until she died.

Answer

Hello again Pelin,

The difference here is in meaning. 
1st sentence: You were her only family member/friend until the time she died.
2nd sentence: You were the only one who was at the same place, at the time she died.

Hope that helps.