Should prayer be repeated if a yellow discharge appears after istinja', given the lack of knowledge about its impurity and the possibility of it having exited from deep within the vagina after prayer?

If you doubt that a drop exited after the prayer, then your prayer is valid because the principle concerning an occurrence is to estimate it at the closest time, so it is considered to have exited after the prayer. If you find an indication that it exited before the prayer, your prayer is valid if you were unaware of its presence. However, if the piece is from medicine residue, it does not affect the validity of the prayer even if it is impure. So your prayer is valid, and you do not need to repeat it.