Dumb Question about CBD Oil

Hey everyone, I live in Texas and I'm wanting to try cbd oil for anxiety.

I've tried six different meds prescribed by my psychiatrist for depression and anxiety and none of them have worked. I do not have the money to keep making appointments to play the trial and error game at this time.

I found a representative selling thc-free cbd oil in my area and a shop in my area selling cbd with a very small amount of thc.

So my question is: If I choose an oil with a small-medium amount of thc will it show up on a drug test as if I'm smoking marijuana?