Are these all OK?
Person A - Where are you?

If I say;
I'm close. / I'm close by. / I'm nearby.

Question

Are these all OK?
Person A  - Where  are you?

If I say;
I'm close.  / I'm close by.  / I'm nearby.

Answer

All are correct and interchangeable in this context.

Answer

Yes, they are all correct.

Answer

I guess I might use "I'm close" figuratively, as in "I'm nearly finished something." but not the other two ,as they are always relative to the other person.
.
I've finished the game level. Where are you?
I'm close.