I will now explain some practical techniques that I would give someone in your position. It looks like you have already implemented some of them. FYI I haven’t provided much background on any of the techniques, so if you want any more information on any of the mentioned techniques check out my post on the CFAR material as well.

Value Awareness

• Reframe the situation to find hidden values. You can do this, for example, by asking: “If I was already at the public school would the choice to switch to the private school be just as hard”. If there is a difference, then analysing why can often reveal hidden values.
• Use goal factoring to find hidden values. This entails finding some alternate set of actions through which you could get what you want cheaper and then analysing why you don’t choose to go with the cheaper option. For example, boarding at the school would resolve move of the problems you have, e.g. travelling and not having enough social time with the other students. I don’t know if this is an option, but if it is and you don’t want to do it then the reason for this should be in your considered valuations.
• Find out which aspects of the choice are cruxes. You can do this by creating a list of the valuable or aversive things related to the two choices and then eliminating one of them at a time to see if the choice you would make is significantly altered. If it is, then you have found a crux.
• Reference class hopping. Try and think about if your choice ever wavers. That is, if there are moments when you really want to change schools. If this happens, then it indicates that there may be some large underlying issue that is prompting the desired change. An example might be that your desire to change schools spikes when you are feeling excluded, like you are not part of the clique or like you can’t connect deeply with anyone at the school. A large underlying issue, in my opinion, indicates a problem that you should at least try to resolve before making any drastic decisions.

Prediction Accuracy

• Take an outside view. Can you find anyone who has made the same choice already?
• Trial the change to see what it will actually be like. This is probably not applicable for your situation, but it is normally one of the first things to look into.

Agency

It can often be good to spend most of your effort on thinking about how to fix existing problems rather than moving to a whole new situation. It is common for people to not think about or to underestimate the costs involved with change. In your case, example costs would be having to get to know the new teachers and students in the public school. An example of fixing a problem could be seeing if it is possible to set up a math club at your private school.

• Think through all the cruxes that you figured out earlier and try to come up with as many solutions as you can that would deal with those cruxes. For example, instead of taking the trip to the private school each day you can look into boarding at the school. Once you have come up with these strategies you can take a much more intricate approach to the choice, perhaps, employing multiple strategies to deal with different aspects relating to the choice.
• Get the advice of others especially those who can relate and are close to the problem, e.g. teachers, parents, friends etc. Be sure not to present the solution as a false dilemma, i.e. to change schools or not. Instead try to explain the situation as fully as possible. This could involve going through all the cruxes and the strategies you have come up with the resolve them. There are two extra benefits to this as well:
  1. It can often help you come up with a solution that should have been obvious. This is because there is difference between thinking you have fully understood a problem and being able to fully explain it to another person.
  2. It allows you to see the problem from a different perspective. It can, at times, be easy to miss the ramifications for other people of the choices that we make.