How to play order of cards and triggering effects in Harry Potter Defense Against the Dark Arts
Generally no, it's not allowed.
Once a card's effect has taken place, you can't reverse the decision. As L. Scott Johnson aluded to in his comment, this is something that friends at the table can allow, especially if the outcome hasn't changed because of something that was triggered by the effect.
For example, if you banish a coin to draw another card, and receive another coin. If you had kept the first coin and banished something else you could now have afforded buying a new card so you want to change your mind about what you banish. At this point you've cheated by looking at what will happen in the future depending on what you decide to banish. That's like looking at the top card before deciding what you want to do.
In your example however it more comes down to a gentlemans agreement since the card you banished doesn't affect what you were allowed to do while it was in play. So I wouldn't be surprised if your opponent allows it if you ask.
I would personally however say that this is a good lesson in tactics and use it to learn how to plan what you need to do in a turn to minimize mistakes like this.