The new IV order should have been written as a SEPARATE order (not just +3) with clear start and stop dates. Maybe the order could read: Continue IV...times 3 doses.
The PO ATB should have been written with a CLEAR start date (and shift/time if need be). If it was a paper MAR it should even have the date marked and previous dates crossed through.
Anyway, you are not the one that GAVE the med incorrectly, so, yes it is technically not your error. However, writing the new order VERY clearly could prevent this.
I do not know the line you signed, but it is not your error.
Also, when in doubt about a new order, ask another nurse, even at change of shift.
Don't worry, you will learn these things with time.